“Knife skills are very underappreciated,” he mused with a sigh. “And yet, we have all these expensive knives out there. …” He shook his head at this sign we’ve all gone off the deep end, culinarily speaking.

Mr. Waxman opened the perpetually packed, “Italian-influenced” Barbuto in 2004. On a recent Friday morning, its massive garage-door walls open to the breeze and sunlight and its tables spilling out onto Washington Street, the restaurant felt like a paradise quite apart from Manhattan. Mr. Waxman was attempting to teach a hapless visitor how to make his Three-Tomato Salad (see recipe at right), which, despite involving very few ingredients, was proving difficult. Mr. Waxman trained in France after abandoning hopes of a career as a jazz trombonist at age 26, and ever since, he has prized two things in his restaurant kitchens: quality ingredients and technique. A proper salad therefore requires only that you get the best heirloom tomatoes within a 250-mile radius of New York (Mr. Waxman does not go for “FedExed food”) and that you cut them right.

There is more to this latter part than you’d think, but Mr. Waxman, now age 56, was a patient, if exacting, instructor, even as he moved restlessly about the kitchen. His staff streamed in and out, seeming less like members of a world-class restaurant team than like hip young neighbors. He greeted them good-naturedly. (“There’s my chef. He’s waking up!” Mr. Waxman crowed as a sleepy-eyed Justin Smillie—tall, blond, 30-ish, clad in polo shirt and cargo shorts—shuffled in. Mr. Smillie paused to greet us before heading to the Union Square Greenmarket for the day’s vegetable haul.) The smell of freshly baked focaccia started to permeate the air as a couple of cooks manned the kitchen’s large wood-burning oven, preparing for lunch. The hostess set out picnic-y red gingham napkins on the industrial-looking wood tables. Above the bar, from a large mock-up of his new cookbook, A Great American Cook: Recipes from the Home Kitchen of One of Our Most Influential Chefs (out September 12 from Houghton Mifflin), Mr. Waxman presided over the scene with a warm, slightly mischievous smile, sipping a cup of espresso.

Was this really his office, one had to wonder? Could a person spend his day like this in Manhattan—standing in an open-air kitchen, slicing ripe tomatoes in the breeze? “We had to do a lot of work to get it to where it is now,” said Mr. Waxman of the space, a former Rolls Royce garage that was leased in 1991 by his now business partner, the photographer Fabrizio Ferri (who lured Mr. Waxman to Washington Street to open the restaurant after they coincidentally moved into the same building and became friendly). One cannot imagine mornings so leisurely paced and glorious at, say, Daniel. I was reminded we were in New York only when Keith McNally drove by, presumably on his way to work. “See you tonight!” called out Mr. Waxman with a wave (he was eating at Balthazar later, he explained).

MR. WAXMAN IS A CALIFORNIA TRANSPLANT and onetime Alice Waters protégé. He opened his first New York restaurant, the acclaimed and popular Jams, in 1984, and more recently owned Washington Park—also beloved while it lasted—in the space that is now Cru. Mr. Waxman is tan, rumpled and considerably leaner than he appears on the cover of his new cookbook, but he’s a towering figure among his peers and the city’s in-the-know foodies, often credited with introducing “California” cooking—which involves grills, fresh ingredients and simplicity—to the East Coast. As Bobby Flay puts it in the book’s foreword: “The mid-1980s brought the food revolution to America—and I was working for one of its generals.” Mr. Waxman has also mentored, among many others, Joey Campanaro of The Little Owl, Jimmy Bradley of the Red Cat, and Aaron Sanchez of Centrico, whom he called “his adopted son,” adding, “I have a lot of adopted sons.”

Yet Mr. Waxman does not cultivate the public persona of a Tom Colicchio or a Jean-Georges or even a Danny Meyer. And why would he? The focus of his entire project as a chef—and, in a way, the foundation of his larger worldview—is his ingredients, and to that end, he’s quick to deflect attention off himself and onto the growers, fishermen and farmers who supply him with its raw materials each morning (Barbuto is on the “zero-inventory plan,” he explained, meaning food is brought in every morning and cleaned out entirely by night). They can be a “disorganized” bunch, he said of his suppliers, but he works hard to cultivate relationships, ensuring a constant stream of fresh local ingredients into New York City—this least bucolic of places. “There’s nothing better than going right from the yard to the table,” he said. “These tomatoes were probably picked yesterday or the day before.”

Mr. Waxman can hold forth on the tomato for hours. “Tomatoes are like little babies,” he said. “They always misbehave. They’re very persnickety. If it rains one day, they get mad. Or if it’s not sunny for them, or it’s too foggy, or the wind blows too hard. The farmers are like parents. So it’s easy to make a tomato salad, but the farmers that grew the stuff—that wasn’t easy. It wasn’t that easy to go get them. The easy part is assembling it.” Mr. Waxman buys his astonishing variety of heirloom tomatoes from a few chosen farmers at the Greenmarket (Hawthorne Valley Farm and Ryder Farm Cottage Industries are among his favorites). “Heirloom tomatoes were probably last widely popular in the 20’s and 30’s,” he reflected. “At some point, we all decided we wanted beefsteak tomatoes like New Jersey’s. So all the agricultural departments around the country said, ‘Well, let’s get a tomato that you can pick slightly green, put in a box, and send anywhere in the world.’ And that’s what happened to the tomato industry. To the point where people look at heirloom tomatoes and say, ‘What is that?’ They’re expensive because everyone stopped growing them.” It’s a phenomenon, Mr. Waxman explained, that goes far beyond tomatoes. “Everyone wanted something standardized,” he said. “You know, they wanted red snappers to be this big”—he held up his hands to demonstrate—“so if a red snapper was this big they didn’t know what to do with it. So now we’re kind of relearning everything.”

Mr. Waxman’s is a fashionable approach to cooking these days, but he’s been doing it this way for years. He’s quick to explain that his focus on the purity and quality of ingredients just better serves his flavor (and hey, he’s gotta sell the stuff), and in this way he makes the whole eco-consciousness project sound refreshingly modest. While he’s genuinely concerned for animal welfare, seeking out poultry and veal and beef that has been properly fed and raised, he seems equally concerned for tomato welfare. “I don’t want to eat anything that’s been treated poorly, whether animal, vegetable or fish,” he said, adding, “There has to be some kind of respect.” He comes off not as a zealot, or even an environmentalist, but just as a person of eminent good sense: thoughtful, practical, vaguely surprised that the rest of us are just now catching on to what he’s always known—local food is best.

The rest of us may dote on our miniature Chihuahuas and choose not to contemplate the origins of our dinner, but there is no avoiding where something comes from in Mr. Waxman’s kitchen. It’s the only thing that matters. That, and the knife technique, which ensures that once you are in possession of the perfect ingredient, you actually use the right parts of it. Most people don’t do this, he explained, “which is why there are so many shitty tomato salads.”

MR. WAXMAN DOESN'T SPEND much time cooking at Barbuto anymore—“My world’s a little different now. I put in my years behind the stove,” he said—but he’s at the restaurant most days nonetheless, chatting up the regulars, popping in and out of the kitchen and overseeing the menu, which changes daily based on the seasonal availability of ingredients, all of which he tries to source from within the aforementioned 250 miles of the city (this is possible for everything except olive oil and wine, he said. Olive oil because they don’t make it in these parts, and wine because “if I was stuck with the wineries just in New York, I wouldn’t be that happy”). His food, he will tell you, is more the simple sum of the best ingredients than the expression of any sort of culinary genius. Or rather: “Boulud is a surgeon. I’m a pharmacist!” Mr. Waxman thinks of himself more as a “home cook” than a big restaurant chef—hence the name of his book—and he has tried to channel that vibe into his latest publishing effort, which features recipes he makes at Barbuto but also some he makes at home for his three young kids: Everything from Crispy Chicken and Goat Cheese Burritos to Lobster and Potato Chip Salad to Pizza with Bacon, Scallions, Parmesan and Tomato.

The prevailing sense is of a man who loves to cook, and who has spent upwards of 30 years laboring contentedly away at his life’s calling. Food, he thinks, should be a casual, participatory social experience. He has little use for the “chemist” chefs currently fixating the international food scene, disciples of Spain’s Ferran Adrià, who have popularized the idea of foam-as-food. “I’m intrigued by it from an intellectual point of view,” he said. “And I’m the last person to want to stymie creativity. But I also fundamentally believe that there should be as few steps as possible—that it should come from the field to the plate with the least amount of fuss. I think people are going to come around to the way I think. I think they’ll get sick and tired of it.” And while he claimed he would be nowhere without his French technique, Mr. Waxman still departs from the Jean-Georges’s and Daniel Boulud’s of the world in one important way: “In the old days, if you’d go to Bouley, you sit down and eat from six to twelve,” he said. “I’m sorry, but I don’t want to eat that long. The last concert I went to was Sun Ra’s Arkestra, and that was six hours, and that was too long for me, too! The whole religious aspect of dining—I’m over it.”

Which brings us back to our salad: laboriously, if clumsily, cut; casually assembled and jumbled together by hand; and then, while Mr. Waxman watched carefully, drizzled in olive oil and balsamic vinegar and “broadcast” with sea salt (the recipe calls for red wine vinegar, but Mr. Waxman believes in improvising, and besides, he had great balsamic that day). He had his chef whip up some pizzas as an accompaniment, and we hunkered down at the picnic-style table in the middle of Barbuto’s kitchen—which Mr. Waxman said he seats twice a night—to eat. It all suddenly seemed rather easy. The Greenmarket, the slicing, the drizzling: Farm cooking in Manhattan! It was, we think, the best pizza and tomato salad of our life. Was it just that we were sitting right in the kitchen, 10 feet from the oven? Was it the breeze? Or was it the tomatoes, which an hour earlier had been sitting over on 14th Street at the market? Mr. Waxman clearly had his ideas. “I’d rather drive 100 miles to the farm, pick up squash, eggplant, strawberries, pile in the car with it all, bring it back, throw it on the table and cook it than go to Whole Foods,” said Mr. Waxman, reflecting on his ideal meal scenario. “But that’s just me.”