Henry Winkler appeared on The Late Show With Stephen Colbert to discuss his new memoir, Being Henry: The Fonz…and Beyond.

Winkler’s book, published Tuesday by Celadon, tells the story of his life and career as the actor who played the characters Arthur “Fonzie” Fonzarelli on Happy Days and Gene Cousineau on Barry. A critic for Kirkus wrote of the book, “This charming autobiography of personal struggles during times of career success and challenge deserves a big thumbs-up.”

After serving Winkler a slice of Bundt cake in honor of his birthday, Colbert revealed that as a child he dressed up as Fonzie for a Happy Days Day at his school.

“You know how incredibly loyal the Fonz has been to me over all these years?” Winkler said. “He gave me notes when he read the book. He cut a lot out. That’s it, that’s as far as I’m going with that joke.”

Winkler went on to talk about the memoir, saying, “I wrote it with a wonderful man named James Kaplan. I’m used to writing books; I wrote all those children’s books with Lin Oliver.…For years, people said, ‘How do you be cool? What is cool? Teach me how to be cool.’ And what I have come to realize is that cool is being authentically yourself. I spent a lot of my adult life being who I thought I should be, and I’m now becoming who I am, and it is freeing.”

Michael Schaub is a contributing writer.