>Yet, “brooch” is the preferred spelling.

for what? a brooch is something you wear at the neck. a subject is broached. they are homophones -- pronounced the same. OED has this note for brooch: Forms: broche, brooche, brouche, brutch, browche, bruche, brouch, broch, bruch, Sc. brotch(e, broach, brooch. [ME. broche; the same word as broach, the differentiation of spelling being only recent, and hardly yet established. Occasionally pronounced (brutch).]

maybe WS is to blame: Georges halfe cheeke in a brooch.