John Travolta: Baby Benjamin Looks Like Me

"I love holding him and feeding him," says the happy dad

John Travolta has a little mini-me: baby boy Benjamin.

“He looks like me,” Travolta, 56, tells PEOPLE of his bright blue-eyed 7-week-old son at the opening of the new Breitling flagship store in New York Thursday night. “He’s been great. One night, he actually slept seven hours – which is unbelievable!”

The downside to having a newborn? Traveling – but only because he’s away from his little boy. Travolta was in Manhattan Thursday, while his family, including wife Kelly Preston and daughter Ella Bleu, 10, were home in Ocala, Fla.

“I’ll be exactly gone 24 hours, and I miss him already,” says the proud dad, who will head to Berlin on Feb. 5, where he’ll be honored with the prestigious Golden Camera award for his movie work.

After enduring the tragedy of losing son Jett in 2009, Travolta is again enjoying the simple pleasures of fatherhood.

“I love holding him and feeding him,” he says of Ben. “My time is bottle time or when he’s contented and ready to be walked around and held or taken for a walk.”

He adds: “Otherwise, he’s on Mom’s breast. So I have to be on call hop in when it’s my turn.”

For more about Travolta’s baby boy, including the exclusive interview and family photo album, pick up the new issue of PEOPLE, on newsstands now