Brooch and broccoli are cousins — both from Latin broccus ("projecting") — and "broach" (to raise a topic) is the same word, meaning to pierce something open.
An ornamental pin fastened to clothing with a hinged clasp. Historically, a functional fastener for cloaks and garments.
From Middle English broche (pointed instrument, pin, brooch), from Old French broche (spit, pointed tool), from Vulgar Latin *brocca (projecting point), from Latin broccus (projecting, pointed, with protruding teeth) Key roots: *brocca (Vulgar Latin: "projecting point, spike"), broccus (Latin: "projecting, pointed").
Brooch and broccoli are etymological cousins — both from Latin broccus meaning "projecting, pointed." The brooch projects its pin; broccoli has projecting flower shoots. The word "broach" (to raise a topic) is the same word with a different spelling — to broach a subject is to pierce it