Brainlessly tells you how someone did a thing: they did it in a completely stupid way, without thinking. “He brainlessly agreed” means he said yes without using his head. The adjective brainless describes a person, an idea, or a rule; this -ly form describes the action. Informal, and still quite sharp — the same blunt feel as brainless. It does not mean the person has a medical problem, and it is not a forever label; it is about one empty-headed move. Though actually, students sometimes mix the two forms and write brainless where English wants the adverb: we say she answered brainlessly, not she answered brainless.