Hugh Jackman and daughter Ava
06/14/2012 at 11:00 AM EDT
Even Wolverine needs a little pampering on Father's Day.
, the X-Men
superstar, admits he gets "pretty spoiled" on Father's Day by his wife Deborra-Lee and his kids
– son Oscar and daughter Ava.
"I get a lot of home cooking, which is great," PEOPLE's 2008 Sexiest Man Alive
, 43, tells Parade
. "My wife is an amazing cook. And my son is actually an amazing cook, too. So I always get a fair bit of cooking on Father's Day."
Jackman, who will star in the upcoming screen musical adaptation of Les Miserables
, also reveals his favorite Father's Day gift – and it beats anything he's ever won for his work in film, theater and television.
"The best is a handwritten card," he says. "I don't know where some of my awards are, but I can tell you exactly where those cards are. I treasure them most."
Jackman also treasures simple family time at home – "everyday moments, like sitting around cooking pancakes together on Sunday morning," he says. But as his kids get older, they're starting to deal with their dad's fame more and more.
"My daughter is 6 and she is really starting to get it now," Jackman says. "My son is 12 and he just wants me to be dad. He doesn't want me to be famous. He doesn't like when people come up to me on the street. He would much prefer if nobody knew who I was."
However, there is a silver lining. "I've seen him in social situations when he didn't think I was listening, and he once said to a girl, 'Well, my dad is Wolverine,' " Jackman says. "So when it came to try to talk to this girl, apparently it came in handy!"