"the body formed in the females of all animals (with the exception of a few of the lowest type) in which by impregnation the development of the fetus takes place," mid-14c., egge, mostly in northern England dialect, from Old Norse egg, from Proto-Germanic *ajja(m) (source also of Old Saxon, Middle Dutch, Dutch, Old High German, German ei, Gothic ada), probably from PIE *owyo-/*oyyo- "egg" (source also of Old Church Slavonic aja, Russian jajco, Breton ui, Welsh wy, Greek oon, Latin ovum); possibly derived from root *awi- "bird."
This Norse-derived northern word vied in Middle English with native cognates eye, eai, from Old English æg, until finally displacing the others after c. 1500. Caxton (15c.) writes of a merchant (probably a north-country man) in a public house on the Thames who asked for eggs:
And the goode wyf answerde, that she coude speke no frenshe. And the marchaunt was angry, for he also coude speke no frenshe, but wolde have hadde egges, and she understode hym not.
She did, however, recognize another customer's request for "eyren." Used of persons from c. 1600. Bad egg in the figurative sense is from 1855; bad eggs aren't always obvious to outward view (there was an old proverb, "bad bird, bad egg"). To have egg on (one's) face "look foolish" is attested by 1948.
[Young & Rubincam] realize full well that a crew can sometimes make or break a show. It can do little things to ruin a program or else, by giving it its best, can really get that all-important rating. They are mindful of an emcee of a variety show who already has been tabbed "old egg in your face" because the crew has managed to get him in such awkward positions on the TV screen. ["Billboard," March 5, 1949]
Eggs Benedict is attested by 1898; various Benedicts are cited as the eponym, and the dish itself is said to have originated in the Waldorf-Astoria or Delmonico's, both in New York. The figure of speech represented in to have all (one's) eggs in one basket is attested by 1660s. The conundrum of the chicken (or hen) and the egg is attested from 1875.
Bumble, bramble, which came first, sir,
Eggs or chickens? Who can tell?
I'll never believe that the first egg burst, sir,
Before its mother was out of her shell.
[Mary Mapes Dodge, "Rhymes and Jingles," N.Y., 1875]