Assuming you already shredded the cheese and cooked the meat, whisk two eggs in a small bowl.
Melt ½ tablespoon of salted butter in a pan over medium heat. Pour the whisked eggs into the hot pan.
While the egg is cooking, spread ½ tablespoon of butter on one side of each of the two slices of bread (using 1 tablespoon of butter). I melted my butter and brushed it on. The eggs are ready for the bread once they are almost cooked but they are still slightly soft/runny. Press the bread onto the eggs BUTTERED SIDE UP.
Cook the egg just a minute or so longer. Using a large spatula, flip the egg and bread in one piece, hence the buttered side of the bread is now face down on the hot pan.
Fold the eggs that are hanging off the edge of the bread onto the bread. If desired, sprinkle with salt and pepper. Place the meats and cheese on top of the egg. (I like cheese on both sides so it holds everything in place better.) Fold the breads so they create a sandwich. Grill on both sides until they are as toasted as you like.
Remove the sandwich from the pan and slice in half. Serve hot.