1580s, "to expose to the action of fire" perhaps (but the sense evolution is odd) from French braser "to solder," in Old French, "to burn," related to brese "embers," ultimately from West Germanic *brasa, from PIE root *bhreu- "to boil, bubble, effervesce, burn." Related: Brazed; brazing. Sense of "to solder" is attested in English from 1670s.
"to make of or cover in brass," Old English brasian "to do work in brass, make of brass," from bræs (see brass (n.)). Compare glaze from glass.