We always called them smushed egg sandwiches when I was growing up !
Now I like to mash up the egg with mayo, salt pepper, a touch of mustard, sometimes I add some hot sauce and maybe some paprika.
I love it on wheat toast. I like it in a pita too ! Occassionaly I will add a slice of my favorite cheese (my favorite cheese is whatever I have on hand at the time !!!) [:D]