For those outside the USA, I regret to inform you there is no such thing as a 'Christmas egg' and no Christmas traditions involving eggs. May I suggest you calling it a Christmas cracker?
USA did not invent Christmas, even if you are right with your statement about 'Christmas eggs', I don't see the point of remarking that you are American as if that will make you some sort of Christmas authority.
“Christmas crackers are festive gifts that make a snapping sound when opened.” For example, a Christmas cracker could contain a paper with jokes on it, a paper crown, and a puzzle where you have to disconnect two linked ring-like metal pieces.