Brash
early 19th century (originally dialect); perhaps a form of rash1.
wiktionary
Uncertain. Perhaps from Scots brash, brasch(“a violent onset; an attack or assault”). Perhaps also related to Dutch bars(“stern; strict”), German barsch(“harsh; unfriendly”), Danish barsk(“harsh; rough; tough”), Swedish barsk(“harsh; impetuous”).
Compare American English bresk, brusk(“fragile, brittle”).
etymonline
brash (adj.)
"impetuous, rash, hasty in temper," 1824, of obscure origin, perhaps originally American English; perhaps akin to 16c. Scottish brash "attack, assault," or French breche "fragments," especially of ice, which is from a Germanic source (compare Old High German brehha "breach," from brehhan "to break," from PIE root *bhreg- "to break"). Or perhaps akin to German brechen "to vomit." Not considered to be connected with rash (adj.) though they mean the same. Related: Rashly; rashness.