You'll want to pre-toast the bread; otherwise, the egg will be overcooked by the time the toast is properly browned. Melt a tablespoon of butter in a large cast iron or nonstick skillet over medium heat, and cook the bread until it's lightly browned on the bottom side.
Add the Eggs
Add another half teaspoon of butter to the center of each eye, let the butter melt, then break eggs into the holes. Season them with salt. Cook until the eggs can easily be lifted from underneath with a thin spatula.
Flip and Add Cheese
Flip each slice of bread over (carefully!), and place a slice of cheese over each one. Meanwhile, place a folded slice of cheese in between the circular cutouts.
Once the bottoms of both slices of bread are lightly browned, carefully close the sandwiches and cook for another minute or two, until they are deeply browned and the cheese is fully melted.
The Grilled Cheese Eggsplosion
You know you want to make one...
2 slices sandwich bread, 2 tablespoons butter, 2 eggs, and 2 to 3 slices of cheese. I like using a mix of American (for gooeyness) and cheddar (for flavor). You'll also want to have some salt on hand.
Cut the Holes
You can use a fancy ring mold for this, an empty can with both ends cut off (tomato paste cans work great), or the lid to a Mason jar, like I'm using here. Cut a hole out of the center of each slice of bread.