I’ve interviewed Tim Minchin several times, but never in the surprisingly big, hairy and hungover flesh before. ‘I’m totally comfortable on stage but I like to appear discomforted and vulnerable because it works with my material. I’m surprised how effectively make-up hides my slightly chunky, not particularly nice to look at …’ I protest, but he shrugs and simply says of his kohl-eyed, Tim Burtonesque stage persona: ‘He’s just closer to Johnny Depp than I am basically. And make-up works, that’s why people wear it.’

With a career spanning three continents, the Aussie comedy pianist has few reasons to be modest. But after experimenting with various musical genres, from campfire song to beat poetry and nu-rave, he’s contemplating making his sound bigger, indeed following Bill Bailey by appearing with a full orchestra, beginning in Australia in 2011. ‘“You Grew On Me” could be amazingly funny and disconcerting with an orchestra and I want to make songs that are genuinely beautiful and then genuinely jarring,’ he says. ‘So I’ll do that, then write a sort of half-hour musical about a hyper-pretentious, massive orchestrated journey of sorts for my character and get a choir.’

He hopes the character and his shows will grow, outlandishly and Dame Edna-like, to keep pace with his burgeoning popularity, and Minchin speaks wistfully about performing in the style of Elvis Costello or Rufus Wainwright, brimming with comic mischief but not necessarily worried about maintaining a constant rate of laughs. Before that, though, comes his biggest challenge to date. Having suggested the adaptation a decade ago, by complete coincidence he’s been commissioned by the Royal Shakespeare Company to turn Roald Dahl’s Matilda into a musical which is slated to premiere at the end of next year. ‘I couldn’t believe it, this iconic company. The first thing I ever wrote in musical theatre was for Love’s Labour’s Lost, so in a way it’s perfect!’

Usher Hall, Edinburgh, Sat 10 Oct; Pavilion Theatre, Glasgow, Sun 11 Oct