Cheesy Gashouse Egg Sandwich

Cheesy Gashouse Egg Sandwich

4 large eggs
8 slices white, wheat, or egg bread
2 tablespoons butter, room temperature
6 ounces Beecher’s Just Jack or Roth Käse gruyere, coarsely grated
Salt and freshly ground pepper, to taste
Have a small bowl or cup ready.
To assemble: Butter one side of each slice of bread, and place on your work surface, buttered side down. Using a 2 1/4-inch-diameter glass,(such as a juice glass), or a sharp knife, cut a 2 1/4-inch hole in the center of each bread slice. Press the cheese evenly onto 4 bread slices around the hole. (It may seem like a lot of cheese, but you’ll see that it’s the perfect amount. It’s okay if a few bits of cheese are left behind.) Place the remaining 4 bread slices on top, buttered side up.
To cook: Heat a large nonstick pan over a medium-low heat for 2 minutes. Put the sandwiches in the skillet (in batches if necessary), cover and cook for 2 to 3 minutes, or until the undersides turn light brown. Turn the sandwiches and, working quickly, separate 1 egg over the small cup, allowing the egg white to drip into the cup. Pour the yolk into the hole in the bread and then pour the egg white over it. Sprinkle with salt and pepper to taste. Repeat with remaining eggs and sandwiches.
Cover and cook for 2 to 3 minutes, or until the undersides are golden brown, and the yolks have begun to set (the egg whites won’t have cooked through yet). Carefully turn the sandwiches again (some of the egg white may run off since it is still partially uncooked. Cover and cook 1 to 3 minutes, depending how you like your eggs. Cut the sandwiches in half diagonally and serve right away.
Note: This sandwich cannot be made in a sandwich maker. It can be made on a grill if you use a pan. If you choose to do this, follow directions above for the stovetop method.