"pointed instrument," c.1300, from O.Fr. broche "spit for roasting, awl," from V.L. *brocca "pointed tool," orig. 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 and spurring into action (cf. O.Fr. brochier "to spur"); from the same source as broach (n.).