From be- + smart. Compare English besmarten, Scots besmerten.
besmart (third-person singular simple present besmarts, present participle besmarting, simple past and past participle besmarted)
- (transitive) To cause to smart all over.
1844, Thomas Jackson, The works of Thomas Jackson:
Yet if any will say that I have put fire thereon, and that they see it flame; I assure them I will make no other use of the ashes, but to make a lee to besprinkle and besmart my own and the eyes of such other sluggish Christians, […]