More like Hollandaise sauce (or Béarnaise, with the herbs) instead of mayonnaise. Both will also congeal after cooling down like in the 2nd child pic (because of the butter, and the yolk being partially cooked), so they have to be served warm.

Though I suppose one can technically call these sauces mayonnaise made with butter. And in Chinese all three can be called 蛋黄酱 (literally "egg yolk sauce"). Hollandaise in particular gets called 法式蛋黄酱 ("french-style egg yolk sauce").

Also, the Adventurer's breakfast sandwich is basically eggs benedict.

Edit: Oh wait, we actually have eggs_benedict as a tag.