Browse
late Middle English (in browse (sense 2 of the verb)): from Old French broster, from brost ‘young shoot’, probably of Germanic origin.
wiktionary
Middle English browsen, from Old French brouster, broster(“to nibble off buds, sprouts, and bark; browse”), from brost(“a sprout, shoot, bud”), from a Germanic source, perhaps Frankish *brust(“shoot, bud”), from Proto-Germanic *brustiz(“bud, shoot”), from Proto-Indo-European *bʰrews-(“to swell, sprout”). Cognate with Bavarian Bross, Brosst(“a bud”), Old Saxon brustian(“to sprout”). Doublet of brut, breast, and brush.
etymonline
browse (v.)
mid-15c., brousen, "feed on buds, eat leaves or twigs from" trees or bushes, from Old French broster "to sprout, bud," from brost "young shoot, twig, green food fit for cattle or deer," probably from Proto-Germanic *brust- "bud, shoot," from PIE *bhreus- "to swell, sprout" (see breast (n.)). It lost its -t in English perhaps on the mistaken notion that the letter was a past participle inflection. Figurative extension to "peruse" (books) is 1870s, American English. Related: Browsed; browsing.