A bro-stache is similar to a "trash-stache." It is a thin layer of peach fuzz type hair that is not fully grown into a full mustache yet. It derives from young latino boys ranging from the ages of 12-20. This age range of young latinos predominantly have these staches and call each other "bros," which is where the term "bro-stache" came from.
Morgan: Woh! Hey Steph, did you just see that kid with the sweet bro-stache?
Steph: Yeah, he looks like such white trash!