The egg itself should be slightly runny, since part of the yolk will be used to moisten one slice of bread. Mayonnaise (Best brand, here on the west coast) can be applied to the other, as liberally or as daintily as you like. The egg white will also be as you prefer, either a bit crisp around the edges or carefully cooked to a uniform doneness. The bread could be the soft, white kind common to childhood, or the multi-grained adult variety. No other condiments or embellishments are needed, other than a sprinkle of salt.
With the first bite, egg will ooze out all the sides, which is to be expected. It is almost impossible to eat this sandwich without licking your fingers, thereby making it one of the foods not recommended for eating at the keyboard.
Like peanut butter sandwiches, it is best made at home.