updated 08/22/2013 AT 11:00 AM ET
•originally published 08/26/2013 AT 2:00 PM ET
It’s been a joy, Pegg tells PEOPLE, but sometimes difficult to reciprocate certain gestures.
“[Chris] sang a song for [Matilda] in Berlin when she was born,” Pegg said, with still-apparent awe, last week at the Los Angeles premiere of his latest film, The World’s End. “He dedicated one of the songs, and I was really chuffed about it.”
And what does Pegg, 43, do for the Paltrow-Martin household?
“Muffins,” he deadpanned. “Any kind of gift basket, maybe some toiletries …”
In fact, food does work, he added. “They eat anything, believe me,” Pegg says with a chuckle. “I go around there with a bag of éclairs every time I see them. They scoff ‘em down, and I don’t even get any.”
While being a godfather has been amazing, Pegg adds that fatherhood to Matilda has been the most transformative experience in his life.
“She’s amazing,” he says. “She’s the center of my life, and I value spending time with her more than anything. She’s the best.”