What is Billy Bob Thornton’s most iconic role? Some may say the taciturn barber in the Coen brothers’ The Man Who Wasn’t There, others might contend it’s the learning disabled killer in his early film Sling Blade. But we all know the truth: it’s the sex-addicted alcoholic Father Christmas in Bad Santa who is obsessed with the “three Bs” (look it up, this is a family publication).

Be that as it may, Thornton has had a stellar Hollywood career since emerging in the mid-90s. Sling Blade, the independent 1996 film he wrote, directed and starred, won him a best adapted screenplay Oscar – though his directing career went into hibernation after a difficult time adapting Cormac McCarthy’s All the Pretty Horses a few years later. However, he became a stalwart of mainstream and independent acting in that period, with roles in Armageddon, A Simple Plan and Monster’s Ball.

Thornton leaned into his raddled screen persona with Bad Santa, turned up as a lecherous US president in Love Actually, reunited with the Coens for the screwball comedy Intolerable Cruelty, and played sports team coaches in Friday Night Lights and The Bad News Bears remake. The rise of high-end TV gave him more strings to his bow: he played a hitman in the series adaptation of Fargo, and a washed-up lawyer in Goliath. And it took him over a decade, but he finally got back into directing in 2012, with the southern drama Jayne Mansfield’s Car. He also has a side-hustle as a singer-songwriter, with four albums to his name – which leads us to his new film, The Trailer Park Boys Presents: Standing on the Shoulders of Kitties – The Bubbles and the Shitrockers Story, which features Thornton and his band the Boxmasters.

So what do you want to ask him as he drops by the Guardian for a reader interview? What does it take to be in a Coen brothers film? What’s it like being a film star musician (and does he compare notes with Johnny Depp)? Any more directing projects on the horizon? Post your questions in the comments below, before Monday 18 November at 12 noon.

• The Trailer Park Boys Presents: Standing on the Shoulder of Kitties – The Bubbles and the Shitrockers Story is in UK cinemas from 10 January