Using a biscuit or cookie cutter, cut a 2-inch hole from the center of both slices of bread. Melt 1/2 tablespoon of butter in a medium nonstick skillet over medium-low heat. When it's melted, add the two slices of bread. Let the bread lightly toast for a minute, or until lightly golden brown, and then flip the two slices over. Dab the remaining butter in the middle of the bread circles. We want to ensure the egg doesn't stick.
Crack the eggs into the holes and season with salt and pepper. If you're using prosciutto, chill with the salt. Just add a little.
Cover the pan for a minute, just until the egg whites are sorta set. Next, add the grated cheese to one half and cover for another minute, or until the cheese is practically melted.
Using a spatula, gently top the cheese slice with the egg slice. Cook for one more minute, or until the cheese is melted.