Zach Braff: Medicine man has the last laugh

"Cereal and no coffee for breakfast at my house. Never a cappuccino or a latte – that was splurging. Then two slices of pizza and a Snapple for lunch. And a falafel sandwich or maybe a burrito for dinner." Zach Braff, star of Scrubs, indie darling of Hollywood and latterly toast of Broadway, is explaining, in some detail, how he used to live on $10 a day, back when he was a fledgling actor. Though it's hard to remember a time when his hapless hospital alter-ego J.D. wasn't wall-to-wall on E4, it was not really all that long ago. In 2000, aged 25, with a sprinkling of plays and small films under his belt and $300 in the bank, he was still waiting tables at a French-Vietnamese restaurant in Beverley Hills. People would come in for dinner straight from the arthouse cinema opposite. "And they would do a double take and say, 'We just saw your movie. We really liked it'. And I'd say, 'Oh, thank you. Now let me tell you about our specials...'"

Cut to 2012 and it's quite a different scene. Eight and half years on Scrubs has made Braff one of the most recognisable, and bankable, faces on American television. (From 2007 until the show ended in 2010, he was rumoured to be earning at least $350,000 per episode). Today, he splashes out on sparkling water, spaghetti bolognese and a cappuccino for lunch. A trickle of fans hover awkwardly by our table and the waitress asks for a picture when she brings the bill. Dressed in expensive layers of grey wool, he's older and less comical-looking than the rubber-faced J.D., almost a little Eeyorish. I'd been expecting a fast-talking, Noo-Joisey wisecracker but he's more a slow-burn, wry anecdote kind of guy, occasionally making himself laugh – a deliberate ack-ack-ack sound somewhere in the back of his throat. He'd make a fine, if lugubrious, stand-up comedian.

For now, though, his focus is elsewhere. Scrubs has given him the means to pursue his "dream life" and go back to where he started – the theatre. He grew up watching his father, a corporate litigator by day, perform in am-dram productions of Hello, Dolly! at their New Jersey community theatre. As a teenager he attended the Stagedoor Manor summer camp where Natalie Portman, Robert Downey Jr and Lea Michele also got their first taste for fame. He was scouted from there, aged 14, to shoot his first television pilot, opposite a young Gwyneth Paltrow – "She was the beautiful high school senior and I was the dorky freshman" – and, aged 18, was cast by his hero Woody Allen in Manhattan Murder Mystery. His first professional adult roles were all on stage – playing Fleance in Macbeth at New York's Public Theatre opposite Alec Baldwin and Angela Bassett, and Romeo at the outdoor Shakespeare on the Sound in Connecticut.

When Scrubs ended In 2010, he appeared on stage for the first time in eight years, in Trust, by the American Pie director, Paul Weitz. In it, he played a repressed, disaffected young millionaire who falls in love with a dominatrix at an S&M dungeon. He enjoyed the experience so much, he was moved to write his own play. The result is All New People, a four-handed black comedy about Charlie, a gloomy thirtysomething who retreats to a luxury New Jersey beach house in the dead of winter to end it all but whose suicidal intentions are thwarted by a string of visitors – a daft estate agent, a drug-dealing fire chief and an escort. Braff, 36, describes it neatly as The Breakfast Club for 35-year-olds. It opened off-Broadway last summer, with Justin Bartha (the groom in The Hangover) in the lead and Braff braced for brickbats. "I'm a guy who has been in a couple of movies and is known for a big broad TV comedy. And there I was bringing my first play right to off-Broadway. I'm no dummy – I knew I had a bull's-eye on my back." In the event, he need not have worried: The New York Times called it "sensationally funny".

Now, Braff is bringing it to the West End, leaving behind the Manhattan loft, where he lives with his girlfriend, the model Taylor Bagley, and their two dogs, Scooter and Roscoe. In London, he will take the lead role. He always wrote the part with himself in mind but for New York was advised to step back and concentrate on his script. "I feel like I know the character quite intimately. It's inspired by aspects of my life. I mean, he's suicidal and I'm not and never have been, thank God. But the emotions and the philosophies are all things that have come from me and my relationships."

Certainly Braff sticks to the adage, write what you know. "Sad Jews in New Jersey are my specialty," he snorts, shovelling spaghetti into that enormous mouth. "You probably aren't going to see me writing a screenplay about CIA agents repelling off a cliff." His debut film as a director, Garden State, was about a disillusioned young actor/waiter returning to his New Jersey hometown. Is All New People a sequel? "This is a different period of my life – being an adult pre-marriage and kids and feeling isolated," he says. "If there is a common theme, it's people rescued by love. I'm a bit of a loner myself. I know a lot of people but I don't necessarily hang out with many people. I have an intimate group of friends. So that's something I write about – at times feeling lonesome."

Really? To the casual observer, Braff lives a charmed life – successful career, homes in New York and LA, model girlfriend, his own plane ("a little one"), even – but he assures me the angst in his writing is autobiographical. "It's very silly to think that because you're in the public eye and you have financial success that you don't experience all of the emotions and problems that people without those things have. When you first have a blast of living your life in the public eye, it can be quite terrifying. It made me retreat and become more private – and I have it on a very mild level. I'm not agoraphobic or anything. But I have a nice little nest."

He was brought up in South Orange on a diet of Woody Allen, Neil Simon and professional introspection. His parents divorced when he was at school. His mother, a psychologist, remarried another psychologist, while his father remarried a family therapist. One of his earliest memories is of playing with his train set in the basement while his parents treated screaming couples in the living room above. "I couldn't really understand their problems but I was very aware of emotion and angst as I made the train go round the tracks." He tilts his head up at the ceiling, J.D.-style. Does he think it made him a better writer? "I don't know. But it has made me who I am and made me interested in psychology and in questioning happiness." His three older siblings are also creative – Adam and Josh are both writers while Shoshanna is a fashion designer.

J.D., the dreamy, pratfalling junior doctor he played for nine seasons of Scrubs, was a heightened version of himself, he says. "Bill [Lawrence, the writer] loved the fact that I know very little about sports and went to theatre camp. So he folded that right into J.D". He thinks they were right to end the show when they did. "I do miss going to work with my friends every day. Cracking each other up as your job is a pretty cool job." He is still best friends with Donald Faison, who played Turk. The two went to Hawaii together at New Year – "With our girlfriends, not alone, much to some fans' dismay." Their "guy love" was the heart of the show and the original bromance. "We never really got credit for it, but I like to think so. By the end, it was like, 'So wait, are they gay or not?' It was a little too much," he smiles. "After eight and a half years the line between J.D. and Turk and Zach and Donald was a little thin."

Now, he's keen to leave J.D behind. He has starred in a low-budget Canadian thriller, The High Cost of Living and has just finished shooting Sam Raimi's blockbusting Wizard of Oz prequel, in which he plays the assistant to James Franco's Oz, with Michelle Williams, Mila Kunis and Rachel Weisz as the witches.

Most of all, he wants to make another film this year, possibly of All New People. He should have an easier time than he did first time round. He spent years hawking Garden State around Hollywood but "everybody in town passed on it". Eventually, Gary Gilbert – "my sugar daddy" – offered to stump up, if Braff cut the budget in half. So he made it for $2.75million and it took $35m.

Woody Allen remains the one he'd like to emulate. Did the director offer the 18-year old Braff any advice that has stuck with him? "He said, 'You know why I named your character Nick?' and I'm like, 'Why?' thinking I'm about to get this amazing piece of knowledge from one of the great auteurs of all time. And he says, 'Easy to type'." Braff slurps the last dregs of his cappuccino and laughs – a slow, satisfied ack-ack-ack.

'All New People': Manchester Opera House, tomorrow to 11 February; King's Theatre, Glasgow, 14 to 18 February; Duke of York's, London WC2, 22 February to 28 April (allnewpeople.co.uk)