I ate a lot of egg sandwiches growing up.
Usually egg, over easy or poached with broken yolks served on buttered toast.
Sometimes scrabbled egg severed on toast with mayo.
And a few other ways.
My southern born aunt's favorite....over easy or poached egg with the obvious runny yolk CHOPPED UP and served on buttered toast. Quite amazing!
I don't think I've seen anyone else do it quite the same way.