Place 4 slices of bread on a cutting board. Lay half the cheese slices on the bread. Lay the bacon, tomato, or ham on top of the cheese. Cover with the remaining cheese. Top with the remaining slices of bread and press down slightly.

Heat a large skillet over medium-low heat and melt a tablespoon of the butter. Carefully place 2 of the sandwiches in the pan, and cook until the bread browns and the cheese is slightly melted, about 5 minutes. Turn the sandwiches with a spatula and add a small hazelnut-size piece of butter to the pan. Cook until the other side of the sandwiches is toasted and the cheese is melted, about 3 to 5 minutes more. Repeat with the other sandwiches. (If at any time the bread starts to brown too quickly, lower the heat to prevent the bread from scorching before the cheese melts.) Serve.