Place a cast iron skillet on the stove top and turn on the heat to medium-low heat. Let the pan warm up before you start cooking. The pan should be hot to the touch, but not smoking.
Spread one tablespoon of the butter on one side of the bottom slice of bread. Sprinkle the Parmesan cheese in the hot skillet, spreading it out to about the same size as the bread.
Place the buttered piece of bread, buttered side down, into the pan, directly on the Parmesan cheese.
Arrange the grated cheese on the top side of the bread in the pan.
Spread the remaining tablespoon of butter on the second slice of bread, then place it face up on top of the bread and cheese in the pan.
Let the sandwich cook until the bottom slice is golden brown, and you have a nice Parmesan crust, and the cheese has begun to melt on the inside. Don’t turn up the heat. Low and slow is the way to go. If your cheese isn’t melting, you can cover the pan with a lid to help, but don’t turn up the heat.
Remove the sandwich from the pan.
Sprinkle the remaining cheddar cheese directly in the hot pan, spreading it out about the same size as the bread. Place the sandwich back in the pan, uncooked side down, directly in the cheddar cheese.
Cook until the cheese is melted on the inside of the sandwich, and you have a nice golden brown, cheesy crust on the outside.
Remove from pan and use a serrated knife to cut the sandwich in half. Serve immediately.
