Asking about her ethnic heritage might be a fun way to break the ice. Or it might be creepy. Take your pick I suppose.
I've always done that, ask their last name as a follow up, and then proceed to analyze what their ethnicity might be right in front of them. If they're one of those girls who doesn't know or care about their background they'll likely be impressed with your knowledge (true or not). If they do care they'll be ready to defend it, and talk about it.
Either way you can win, just ask her.
