Spread about 1 tablespoon butter on one side of each slice of bread. With butter side down, top each slice of bread with about ½ c cheddar.
Heat a nonstick skillet over medium heat with 1 tablespoon butter. When butter is melted add two slice of bread, butter side down. Cook until bread is golden and cheese is starting to melt, 2 minutes. Flip one pice of bread on top of the other and continue to cook 30 seconds.
Repeat for the second sandwich, wiping the skillet clean if necessary.