"pointed instrument," c. 1300, from Old French broche (12c.) "spit for roasting, awl, point end, top," from Vulgar Latin *brocca "pointed tool" (source also of Spanish broca, Italian brocca), noun use of fem. of Latin adjective broccus "projecting, pointed" (used especially of teeth), perhaps of Gaulish origin (compare Gaelic brog "awl").
"to pierce," mid-14c., from Old French brochier "to spur," also "to penetrate sexually" (12c., Modern French brocher), from the Old French noun (see broach (n.), and compare Italian broccare). Meaning "begin to talk about" is 1570s, a figurative use with suggestions of "broaching" a cask or of spurring into action (which was a sense of the verb in Middle English). Related: Broached broaching.
To broach a cask is to pierce it for the purpose of drawing off the liquor, and hence, metaphorically, to broach a business, to begin upon it, to set it a going. [Hensleigh Wedgwood, "A Dictionary of English Etymology," 1859]