But even though he’s kicked, punched and shot villains in the past, Matt says his hardest task to date has been belting a teenage girl.
In a key scene in his new movie True Grit, Matt plays a boastful Texas Ranger who takes his 14-year-old co-star Hailee Steinfeld over his knee and wallops her with a stick.
A dad of four daughters, Matt has never raised a hand to a girl in real life so he and the film directors Joel and Ethan Coen took precautions to make sure Hailee was protected.
The star said: “They put a big pad on Hailee’s behind. And we practised. I said, ‘Hailee, does that hurt?’ And she said, ‘I can’t even feel it.’”
Matt is adamant it is a form of discipline he would never practise, saying: “I definitely don’t spank them.”
Newcomer Hailee was picked from a pool of 15,000 for the role. and Matt calls her performance “astonishing.”
It earned her a nod in the best actress category at the Baftas yesterday.
“This character is nothing like Hailee Steinfeld actually is in real life,” he said.
Matt loved being directed by Hollywood greats the Coen brothers in their remake of the John Wayne classic – and reckons he’s the one red-blooded male who hasn’t seen The Duke saddle up with Glen Campbell in the original movie.
Matt said: “When I found out about this one, I asked the Coen brothers if I should go see the original. And they said, ‘Actually, the book is where you should go because we’re not looking at it as a remake of that film, as much as a strict adaptation of this great book’.”
True Grit stars Hailee as a 14-year-old girl who hires a boozy US Marshal named Rooster Cogburn (Jeff Bridges) to hunt down the dim outlaw (Josh Brolin) who murdered her father.
Tagging along on the manhunt is Matt’s lawman, who may be more windbag than wild west hero.
“I am,” said Matt proudly, “a true nincompoop in this movie.”
That’s not to say he doesn’t earn his spurs eventually.
His butch role is a million miles away from his life at home in New York with the five women in his life.
Baby Stella is the latest addition to his family.
There is Isabella, four, and Gia, two, and stepdaughter, Alexia, 12, his wife Luciana’s daughter from a previous marriage. He joked: “I might have to get a male dog.
“First of all, we weren’t planning another one. But once we got over the initial shock, we got into the pregnancy groove again.”
As for being outnumbered in a household of all ladies, Matt admits there’s one drawback.
“I don’t get a lot of time in the bathroom, but that’s OK,” he laughed. “I’m surrounded by beautiful girls. I’m a lucky guy.
“It’s the greatest, though. You never love anybody as much as you love your kid, in the deepest, most abiding way.
“With young kids, it feels like the morning starts at sprint. It doesn’t stop until my wife and I put our heads down on the pillow at night.
“You’re up, you’re awake, you’re changing diapers. You’re never sleeping.”
Matt had to do a bit of schedule juggling to star in Clint Eastwood’s Hereafter, which opens here next month.
Daughter Stella was born in October, prompting director Eastwood to joke that he almost didn’t get Matt because the actor was “so busy siring children”.
“Clint didn’t have to show me a script,” said Matt, who was Oscar nominated for their last film together, Invictus.
“If he said that we were about to do an interpretation of the phone book, I’d say, ‘Where do I sign?’”
In Hereafter, Matt plays a reluctant psychic who has retired because he can’t have a life while communicating with the dead.
Matt didn’t waste much time checking out the afterlife with real mediums.
“I didn’t want to go down that rabbit hole,” he said. “The problem is I’d have to start cold and probably find imposters. That world is peppered with imposters, which is another theme of this movie.
“But I do believe that there is somewhere we all go to, and that there’s some accountability for the things we’ve done here.”
His character in Hereafter tried to lead a normal life by taking up a cooking class.
He and a fellow student, played by Bryce Dallas Howard, share a sensuous scene where they take turns feeding each other while blindfolded.
In real life, however, you’ll never find Matt in a pinny in the kitchen.
He said: “My mother made me cook a meal once a week when I was a kid. As a result, I don’t cook as an adult. But I love to eat. My passion for eating has only increased over the years.”
Hereafter gave him a further opportunity to watch how Eastwood works because Matt also wants to direct some day.
In fact, old pal Ben Affleck and brother Casey are working on a project they hope Matt will direct. “But there’s no script yet.”
When the modest star was named Sexiest Man Alive in 2007, he told voters: “You’ve given an ageing suburban dad the ego-boost of a lifetime.”
And after the success of the Jason Bourne spy thrillers and his Oscar nomination for his performance in Invictus, Matt also has a star on the Hollywood Walk of Fame.
He doesn’t rule out a return to the Bourne series, even though the film company have announced they will make a movie about a younger Bourne – and Matt is not part of it.
However, he doesn’t rule out playing the rogue spy one more time.
Matt said: “They’re making another Bourne movie without me. But that’s not going to interfere with my ability to come back with Paul Greengrass and make another Bourne movie.”
Right now he’s got two more films in the pipeline, including The Adjustment Bureau opposite Emily Blunt.
And this summer he’s gearing up to play the younger gay lover of pianist Liberace.
Liberace will be played by Michael Douglas now that he has beaten cancer.
Matt said: “I just emailed Michael last week and signed it, ‘Your boyfriend’. So we’re ready.”
Fans of Matt and Michael must want to see the two superstars sharing tender moments on screen.
Matt joked: “I’m sure his wife Catherine and my wife Luci do, too!”