Use a large round cutter to cut a circle out of the center of a slice of bread. Grate cheese onto a bowl or plate. Set both aside.
Heat cast iron skillet over low-medium heat. Reduce heat to low, then melt butter in the center of the pan. Add pepper and stir until it starts to fizz.
Sprinkle half of the cheese in a thin layer about the size of your slice of bread in the bottom of the skillet.
When the cheese bubbles and melts, press the bread down into the skillet.
Crack the egg into the hole in the center of the toast. Sprinkle with additional pepper and pinch of salt, then add remaining cheese on top of the bread and egg.
Cook 2-3 minutes over low heat until the egg white is mostly opaque and set (it will sink slightly) and the bread doesn't squish when you try to slide a spatula under it.
Flip toast, and cook an additional 1-2 minutes until egg white is no longer jiggly and yolk is cooked to desired doneness. For a firmer egg yolk, cook for 2-3 minutes after flipping.A thermometer inserted into the egg white should read 145°-155°F.