I only know a little Korean, but I'm pretty sure that your cousin said, "너 한국 말해" or "너 한국 말해?" (Or maybe 한국말 해.) 1) You speak Korean. 2) You, speak Korean! 3) Do you speak Korean?

"너한국말 해?" means "Do you speak korean?" or let's say "Can you speak korean?"/ You speak Korean?"