Egg, like beg, leg, and other words where “short e” precedes a “hard g” sound, is pronounced with the vowel

[e] /ɛ/ of bet and let, except in parts of New England and the South Midland and southern U.S., where these words are frequently said with

[-eyg], /-eɪg/, to rhyme with vague and plague, especially in the speech of the less educated. This raising of

[e] /ɛ/ to a higher vowel

[ey], /eɪ/, articulated with the upper surface of the tongue closer to the palate, also occurs before

[zh], /ʒ/, as in measure, pleasure, and treasure.

Did you mean egg on one's face?