who painted on a big board beside the road?

Doctor T. J. Eckleburg

But above the gray land and the spasms of bleak dust which drift endlessly over it, you perceive, after a moment, the eyes of Doctor T. J. Eckleburg. The eyes of Doctor T. J. Eckleburg are blue and gigantic — their irises are one yard high. They look out of no face, but, instead, from a pair of enormous yellow spectacles which pass over a nonexistent nose. Evidently some wild wag of an oculist set them there to fatten his practice in the borough of Queens, and then sank down himself into eternal blindness, or forgot them and moved away.