Brusque comes ultimately from bruscus, the Medieval Latin name for butcher’s broom, a shrub whose bristly, leaf-like twigs have long been used for making brooms.
Bruscus was modified to the adjective brusco in Italian, where it meant “sour” or “tart.” French, in turn, changed brusco to brusque, and the word in that form entered English in the 1600s.
English speakers initially applied brusque to tartness in wine, but the word soon came to describe a harsh and stiff manner, which is just what you might expect of a word bristling with associations to stiff, scratchy brooms.