Browch was first introduced on the Adam Sandler movie, "Just Go With It." It appeared to be someone who had a "loose" eyebrow, one slightly elevated from the other eyebrow. However, more recently this word is being used as a combination of "ouch" but with your eyebrow raised therefore you would say "browch."
When a person has a deep interest or sexual preference towards Indian or South Asian (brown) individuals. This term should only be applied to individuals who not only have a 'type' leaning towards Indian individuals, but one that fetishizes the culture associated with South Asia.
It is basically like yellow fever but for South Asians specifically.
Guy 1: Yooo that Indian chick over there is fine
Guy 2: Shut up, you think all Indian chicks are hot, you have a serious case of brownchitis