The Collaborative International Dictionary of English v.0.48:
eye-beaming \eye-beaming\ n. a radiant glance of the eye; as, he pretended profundity by eye-beamings at people. [WordNet 1.5]WordNet (r) 3.0 (2006):
eye-beaming n 1: a radiant glance of the eye; "he pretended profundity by eye-beamings at people"