Early on in our relationship, Nicole and I noticed how I (the 1.5-generation, 'model minority immigrant') always used "Korean" or "Korean-American" when describing myself to someone else. Similarly, I would always throw in her race ("Black" or "African-American") when I found myself describing her to a friend, a colleague, a stranger, a homeless dude on the street.
Often, a person's race or ethnicity has been, continues to be, and will most likely remain the FIRST adjective or descriptor (if not 2nd or 3rd, albeit only in those rare occasions when some other characteristic is so damn unique) I use in describing or referring to someone.
"Remember my friend Manny? The Hispanic kid you met a few months back, the one who quit law school to join a start up?"
"Yo man... Chan-soo has some crazy ups for a Korean kid."