Heat a nonstick or cast-iron skillet over medium-low heat.
Spread one side of each piece of bread with a small amount of softened butter. Sprinkle 2 tablespoons of the Parmesan on each slice so it sticks to the butter. Turn one piece over and sprinkle the mixed cheese on top (this will be the filling). Place the other piece of bread on top, with the Parmesan side facing up.
Carefully transfer the sandwich to the skillet and cook on both sides until the middle filling is melted and gooey. Watch carefully so the surface doesn't burn; it should be a nice deep golden brown. Slice in half and dig in!