Begin by laying 2 slices of sourdough bread on a clean cutting board or work surface. On each slice, layer two pieces of sharp Cheddar cheese followed by the thinly sliced apples. Top with an additional slice of cheese and cover with another slice of bread, pressing down gently to secure the layers.

In a large skillet, melt 1 tablespoon of unsalted butter over medium-low heat. Carefully place the assembled sandwiches into the skillet and cook until the bread is golden brown and the cheese has begun to melt, which should take approximately 3 to 5 minutes. Utilizing a spatula, flip the sandwiches over, adding the remaining tablespoon of butter to the pan. Continue to cook until the second side is also toasted and the cheese is fully melted, about 3 minutes more. Adjust the heat as necessary to prevent the bread from burning before the cheese has melted completely.