Haha true! Googling Elizabeth’s raw eggs seems absent but probably some people do that. By the way she call it "omelet Molière" but I can’t find that recipe in any French cookbook, I guess it’s her creation. However "œuf (egg) Molière" is a classic, but has nothing in common with an omelet but the egg.
you don't put extra raw eggs in it, you simply don't fully cook it on the reverse side of the pan and then fold it so the uncooked egg oozes out somewhat.
mine is hers, except i whisk the eggs more before putting them in the pan