I always pronounced it “brerSHEET”, or if in very frum/ashkenazi company, “BrayShis”...
I never really know how to pronounce anything because the variations are all over the map!
I suppose they key is to be consistent by using one speech family, but yikes, lol.
Imagine a foreigner using English pronunciations that are a mixed bag of NY, British, Yankee, Southern and Midwestern accents, and oh how about Hawaiian too.
Hilarious. Maybe that IS the idea. :)