"pointed instrument," c.1300, from O.Fr. broche (12c.) "spit for roasting, awl, point end, top," from V.L. *brocca "pointed tool," originally fem. of L. adj. broccus "projecting, pointed" (used especially of teeth), perhaps of Gaulish origin (cf. Gaelic brog "awl").
"begin to talk about," 1570s, from figurative use of the lit. meaning "to pierce" (early 14c.), with suggestions of "broaching" a cask or spurring into action (cf. O.Fr. brochier, 12c., "to spur," also "to penetrate sexually"); from the same source as broach (n.).