Tiffany with his Tony.

“I’m always pleasantly surprised when anybody wants to see a production that I’ve directed,” said John Tiffany over the phone from Glasgow two days after the Tony Awards, erasing all traces of false modesty with child-like wonder. “I kinda go, ‘Oh, wow!’ I feel humbled and privileged that people are actually interested. I’ve a strong philosophical belief that works should be accessible and popular—there shouldn’t be obstacles to anybody being able to connect with what you do—but I wouldn’t say I have a mainstream commercial gene in my body at all. All I know how to do is tell the stories in the most accessible way possible.”

That, apparently, is enough: His Once was Tony king at the recent ceremonies, raking in eight awards in all—among them those for Best Musical and Best Director.

Music has always been a key component in Mr. Tiffany’s theatrical pieces, but never before had he attempted a musical per se—let alone one that could be considered “a Broadway musical” and would compete as such and actually win, leaving whole chorus lines of energetic evangelists and high-flying newsboys-on-strike in the dust.

Once has none of the gaudy trappings of traditional Broadway musicals. If anything, it wears its source like a flag—a quiet cult film of 2007 where Guy (a Dublin busker) and Girl (a Czech immigrant) meet, make beautiful music together but not, bitter-sweetly, a lasting relationship. Notable among the songs is “Falling Slowly,” a ballad of soaring urgency that won the Academy Award. The rest of the score, written by the two leads (Glen Hansard and Marketa Irglova), is a haunting, surging dirge to the finish line. No glitz. No buck-and-wing. No 11 o’clock number.

Mr. Tiffany hadn’t seen the film when he was first approached about doing its stage facsimile. “I was with a friend back in Glasgow, who said, ‘You will love the music,’ so the first thing I did was download the album. Loved it. Then, I watched the film.”

One scene in particular triggered a childhood flashback and prompted him to do the project: “Glen takes Marketa to a party where everyone’s sitting around doing a song, and that reminded me of when my dad used to play in a brass band back in Yorkshire,” he said in the press room at the Tonys. “He would take me along on some very drunken evenings with his bandmates and everyone would do their song. There’s something about the way working-class men can communicate through music in a way they can’t in words.

“I thought, ‘Wow! I wonder if we could get that going in the play.’ That’s when I came up with the idea of having a bar on stage—the actors singing as the audience arrives, then the audience going on stage and being able to get a drink from the bar. That was my first thought, and that’s what happened. It took quite a lot of pushing to get that on Broadway—‘Audience on stage? What?’ ‘Liquor on stage? What?’—but we got that. It was an open bar on the first night at New York Theatre Workshop, and Alan Cumming asked me, ‘Is it not a free bar every night?’ I said, ‘Alan, you just think every bar’s a free bar. It’s like the Queen thinks everywhere it smells of fresh paint.’”

He told The Observer over the phone, “We were amazed 1) that the show transferred to Broadway in the first place, and 2) that we were nominated for 11 Tonys. I keep saying to the cast and company and creative team, ‘We’re so lucky in that we’ve made the show we’ve wanted to make.’ We couldn’t be prouder of it and the way it connected with its audience. Then, to get this kind of recognition and acknowledgement for doing our job is just fantastic.”

Mr. Tiffany’s voice broke a bit as he pressed on. “The best thing about it is that it made my mum and dad really proud. My dad’s a kind of quiet Yorkshire man. He doesn’t give away compliments too readily. I spoke to him the morning after the Tonys, and he said he’s never been prouder in his life, and that meant a helluvah lot to me.”

Nobody noticed, but, when Mr. Tiffany accepted his award, he was wearing his roots in his lapel—a dainty white flower from Yorkshire. He meant it as a sentimental salute to his parents, “who gave me the gift of music. They weren’t musicians—my mum was a nurse, my dad was an engineer—but they both had music as hobbies, and I grew up with music. There was something about Once and the process of working on it that made me really connect to home. I live in Scotland now, but I spend a lot of time in America, and I just thought I want to wear something from Yorkshire.”

Otherwise, the 40-year-old deputy director of the National Theatre of Scotland looked very much like a stranger in a strange land—which indeed he was, jetting in just for the awards and then back to Glasgow the next day. He was steering his pal, Mr. Cumming, through Macbeth—all the roles in Macbeth—and left him after the final dress rehearsal in possibly the biggest multiple-personality pile-up since Sybil.

“I wasn’t sure I was going to be able to come because we were right in the middle of the creation process when the Tonys were happening,” Mr. Tiffany said. “If I wasn’t co-directing this with Andy Goldberg, I wouldn’t have been able to come—but, luckily, I was, I could, and I did. It was an absolutely fantastic night. The really great thing about New York theater life is that, if they like you, by God, they let you know!”

This one-man, 100-minute Macbeth—which premiered June 15 at Glasgow’s Tranway Theatre and will transfer to New York’s Rose Theatre July 5-14 as part of this year’s Lincoln Center Festival—is the result of “a meeting of three minds”: Mr. Cumming’s, Mr. Goldberg’s and his. And, yes, as a matter of fact, the actor did come first.

“Alan approached me at the beginning of last year and asked, ‘You fancy doing Macbeth?’ He had the idea that the actor playing Macbeth (i.e., him) and the actress playing Lady Macbeth could swap parts every other night since there’s so much language and talk about masculinity and femininity, so we did a reading in New York. A good friend and collaborator of mine, the New York-based director Andy Goldberg, came to the reading, and afterward we were talking. He said, ‘I always thought a one-man version of Macbeth set in a psychiatric hospital would be great.’ That idea got us both suddenly excited, so we took it to Alan, and he went for it.”

They were preaching to the converted. The first Shakespeare that Mr. Cumming ever read was Macbeth—plus, he hails from Aberfeldy, in Perthshire, Scotland, where the play’s place names (Bertram Woods, Dunsinane) are a hop, skip and jump from home. Such a contagious kinship to the characters almost insisted he play them all.

“You kinda have to see the show to see what Alan is doing—it’s incredibly fluid and subtle,” said Mr. Tiffany of the multitasking. “When we first meet him, he’s just arrived at the psychiatric hospital. Then, he starts to inhabit the characters and stories of Macbeth. As the production progresses, the reason he’s doing that becomes clear. There are no costume changes, no props as such. He’s trapped in this room.”

This is not Mssrs. Tiffany and Cumming’s first time at the gender-bending rodeo. Three years ago to the day of the Macbeth opening here, their National Theatre of Scotland version of The Bacchae bowed at the Rose and was a pretty rippin’ go at Euripides.

As Dionysus, that overheated hedonist and God of Good Times, Mr. Cumming made a rock-star entrance—handcuffed, dangling upside down by his ankles from the flies at the top of the theatre, wearing a kilt (and you know the old rumor about kilts).

Mr. Tiffany also tossed him the perfect one-liner when Dionysus overreacts and incinerates a whole set in a pique: “Too much?” he asks as an afterthought. (Fire marshals monitored the scene carefully, and a flash of heat warmed audience faces.)

Startling the audience is a specialty with Mr. Tiffany. In Black Watch, his stunner about a Scottish Army regiment in Iraq, soldiers make their entrance by ripping their way through a pub pool table. It won 22 awards, including an Olivier for his direction.

One of the people Mr. Tiffany specifically thanked in his Tony acceptance speech was Steven Hoggett, who, billed as “Associate Director,” kept the Black Watch cast in a sweaty state of perpetual motion with marches and military drills. Once gives him credit for “Movement,” and Peter and the Starcatcher calls him “Choreographer.”

“I’ve known Steven for 25 years,” said Mr. Tiffany. “Our kind of collaboration in life and work has been sustaining in so many inspirational and amazing ways. He’s incredible. His form of choreography and movement is, I think, truly innovative.

“Theater is so much more than just walking into an auditorium and sitting down and letting the curtain go up. It can be anything and anywhere, and I think we, as theater-makers, should start celebrating the ‘liveness’ of our form. Theater starts from the moment someone has the idea to go see a performance. Then, it’s about where to buy the ticket. It’s about how much that ticket is. It’s about what the marketing is, what the publicity is. It’s about where the nearest bar is to get a drink afterwards. Theater is a social experience from the first moment you hear about the possibility of going, and we need to celebrate every single element of that social experience. If that involves letting an audience go on stage during a big music session and have a drink from the set bar—and if that makes them more alert to the possibility of what that story might be or what theater can be—that excites me.”

The unifying theme of Mr. Tiffany’s shows is that they don’t unify at all. “They’re incredibly disparate,” he pointed out with some justified pride. “Theatre is a medium that can’t be digitalized. You actually have to buy a ticket and come into a space to see what we do. We really have to explore and exploit that sense of live experience.”

Seating was on the sidelines for Black Watch, bracing audiences for some theater different from what they’re used to. With Once, they go on stage and knock back a few. Macbeth has a comparable thing going. “I really like playing with audiences’ expectations, with their experience of what the event is,” Mr. Tiffany admitted. “Theater-makers should create work that is unique, that can only exist for an audience. Always, always, always think about your audience. The only thing you’re doing it for is an audience. Develop a generosity of storytelling and a desire to connect.”

editorial@observer.com