This is about the adjective abrew, not the verbal form abrewing. It doesn’t seem to be in any dictionaries, but that just means it hasn’t been attested often enough to seem worth spending lexicographers’ time and effort to include. It’s a perfectly good word, if you ask me, since it’s well formed and instantly understandable, and I imagine it’s cropped up every once in a while (as for instance here: “Something new abrew at Gil’s.” It’s an instance of the prefix a- as described by the OED thus:
2. ME. a-: OE. an, on, prep. See A prep.1 above. With nouns, in, on, engaged in, at, in loose combinations, which are really two words; as abed, ashore, afield, asleep, alive. With verbs, adverbs, and prepositions, more closely combined both in form and sense, as aknow, ashame, afore, among, across.