Turn oven on high broil.
Cut a hole in the center of each slice of bread using a cookie cutter (any desired shape) and spread butter onto each side.
Heat a large pan to medium heat and add bread. Crack an egg into each hole, season with salt and pepper. Cook until bread becomes brown and toasted.
Sprinkle Parmigiano Reggiano on both sides and place under broiler for 1-2 minutes.