in cookery, "dish based on eggs beaten lightly and browned in a pan," sometimes with additional ingredients, 1610s, from French omelette (16c.), a metathesis of alemette (14c.), an alteration of alemele "omelet," literally "blade (of a knife or sword)," which is probably a misdivision of la lemelle (mistaken as l'alemelle), from Latin lamella "thin, small plate," diminutive of lamina "plate, layer" (see laminate). The food so called from its flat shape.
The proverb you can't make an omelet without breaking eggs (1845) translates French On ne saurait faire une omelette sans casser des oeufs. As a word for a similar thing, Middle English had hanonei "fried onions mixed with scrambled eggs" (mid-15c.).