If not using leftovers, hard boil the eggs according to the Perfect Hard Boiled Eggs, Steamed Hard Boiled Eggs, or Instant Pot Hard Boiled Eggs methods. Roughly chop the hard boiled egg. Shred the cheese. Thinly slice the green onion. Slice the bread. Spread one side of each bread slice with mayo. Place one slice on a griddle or in a skillet, mayo side down, then, top with half the shredded cheese, the chopped egg and sliced green onion, then the remaining shredded cheese and bread slice. Cook until the bread is golden brown and toasted, then flip and cook a few minutes more until the second bread slice is toasted and the cheese is warm.  Slice in half and serve immediately.