The phrase "hadst egg on face" is an archaic version of the modern "have egg on one's face," meaning to be embarrassed or humiliated. The use of "hadst" instead of "have" indicates a past tense form in Early Modern English. The pronunciation of "hadst" is [hædst] with the initial "h" sounded and the "a" as in "cat." The word "egg" is pronounced [ɛɡ] with a short "e" sound and hard "g." The phrase is often used in informal contexts and can be traced back to the early 1900s.