Fry the egg with 1/4 tablespoon of butter on a pan on medium heat until over hard or over medium, whichever preferred.

While the egg is cooking, butter the slices of bread on one side each with the rest of the butter.

Add 1 slice of american cheese to the unbuttered part of the bread, sprinkle with half the cheddar.

Take the egg off the pan and put onto the cheesed bread.

Sprinkle the rest of the cheddar on the egg, top with the last slice of american cheese then the last slice of bread, butter side up.

Cook the sandwich on pan on medium heat. Wait 4-5 minutes then flip.

Sprinkle the sandwich with parmesan cheese. Flip the sandwich after another 3 minutes and sprinkle the other side with cheese.

Continue to flip into desired darkness of bread.

Put on plate or cutting board and cut in half if desired. Let cool, then enjoy!