Preheat a griddle or nonstick skillet to medium-low. Spread 2 teaspoons of the butter on one side of a bread slice. Repeat with the remaining butter and bread. Place one of the slices butter-side down and shingle the cheese on top, covering the entire surface. Top with the other slice of bread, butter-side up.
Place the sandwich on the griddle and cook until the bottom is golden brown and crisp, 3 to 4 minutes. If the bread is browning too quickly, shift the griddle off the heat. Flip the sandwich, then cover with a small metal bowl and cook until the bottom is golden brown and the cheese is melted, 3 to 4 minutes. Once golden brown on both sides, toast the edges of the sandwich, if desired. Transfer to a cutting board, cut in half on the bias and serve immediately.