Fry the eggs in a non-stick skillet over medium heat, melt butter (1 teaspoon per egg) until it starts to bubble. Crack eggs directly into pan, being careful not to break yolks. Sprinkle eggs with a little salt, add a teaspoon or two of water (per batch) to the pan, and cover. Cook as desired (3 minutes for soft eggs, 4-5 minutes for firm). If necessary, work in batches, wiping out skillet in between each batch and adding more butter and water if necessary.
To make sandwiches; Divide cheese among half of the bread slices and top with an individual fried egg.
Butter the outside of the bread and place sandwiches on a cookie sheet and cook until golden brown. Flip sandwiches and cooker for a little while more until golden brown and cheese has melted.