"shrubbery, small trees and shrubs of a wood; branches of trees lopped off," mid-14c., from Anglo-French bruce "brushwood," Old North French broche, Old French broce "bush, thicket, undergrowth" (12c., Modern French brosse), from Gallo-Roman *brocia, perhaps from *brucus "heather," or possibly from the same source as brush (n.1).
adjective suffix, "full of or characterized by," from Old English -ig, from Proto-Germanic *-iga- (source also of Dutch, Danish, German -ig, Gothic -egs), from PIE -(i)ko-, adjectival suffix, cognate with elements in Greek -ikos, Latin -icus (see -ic). Originally added to nouns in Old English; used from 13c. with verbs, and by 15c. even with other adjectives (for example crispy).
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Definitions of brushy from WordNet
covered with or consisting of bushes or thickets; "a bosky park leading to a modest yet majestic plaza"- Jack Beatty;