I was thinking of writing about eggnog, but this word's etymology is unknown. It might be derived from noggin "small drink" or nog "strong ale"; another theory is that it's a contraction of egg'n'grog - grog meaning "alcoholic drink". The earliest citation of eggnog in the OED (1825) has just been antedated to 1774 by Heidi Harley.
egg is possibly from Proto-Indo-European *h₂ewi- "bird". Proto-Germanic *ajjam, Old Norse egg. The Old Norse word supplanted Old English ǣȝ and Middle English ey plural eyren, from the same root.
The verb egg "to incite into action" is from a different PIE root: *h₂eḱ- "sharp". Proto-Germanic *aǥjan, Old Norse eggja.
The suffixed lengthened form *āḱ-ri- became Latin ācer "sharp, bitter", becoming Old French aigre "sour", which combined with vin "wine" to form vinaigre and English vinegar.
The suffixed o-grade form *oḱ-su- became Greek ὀξύς oksus "sharp, sour", and English oxygen.