"She loves him -- she loves being a big sister," Armie Hammer, who stars in Call Me By Your Name, tells PEOPLE at the Toronto Film Festival

Armie Hammer is one proud dad!

As his movie Call Me By Your Name picks up Oscar buzz, the actor stopped by the PEOPLE, Entertainment Weekly and InStyle studio at the Toronto International Film Festival Saturday, where he opened up about how enthusiastically his 2-year-old daughter Harper is taking on the role of big sister.

“She loves him — she loves being a big sister,” Hammer, 31, says. “She loves taking care of him. They just cuddle and she loves being with him.”

Hammer and his wife Elizabeth welcomed Harper in 2014 and seven-month-old Ford earlier this year. The two married in 2010 after being introduced by one of Hammer’s friends.

Credit: AFF-USA

And while the proud parents have their hands full with their two little ones at home, Hammer says that they still try to do romantic things for each other. So much so that he can’t even pick one specific thing he feels is most romantic.

“I don’t even know what the most romantic thing I ever did is!” Hammer says. “My wife and I always try to do sweet things for each other. That’s kind of the mode. I think the most romantic thing you can probably do is try to do something romantic all the so that you can’t be like, ‘Oh, I was romantic that one time!’ ”

Credit: Jenny Gage + Tom Betterton

An acclaimed gay coming-of-age drama, Call Me By Your Name stars Timothée Chalamet as Elio (Chalamet), the teenage son of a prominent professor who falls for his father’s live-in academic assistant, Oliver (Hammer), during a sun-kissed summer in the northern Italian region of Lombardy. It’s set to hit theaters Nov. 24.