Spread butter on one side of each slice of bread, the one that will be on the outside of the sandwich. Scatter all but 2 tablespoons of the cheese on the unbuttered side of one slice. Top with the second slice, so that the buttered side faces out. Heat skillet over low-to-moderate heat. Sprinkle 1 tablespoon cheese roughly in the center of the skillet. Place the sandwich on top. Cook sandwich until golden underneath and cheese browns and crisps, about 2 to 4 minutes. Carefully lift melted cheese and bread onto spatula, sprinkle remaining spoonful of cheese back in skillet, then flip sandwich over on top of it. Cook on the second side until golden and crisp as well, pressing down on it with the spatula to encourage it to all come together. Transfer to a plate, cut in half if desired, and dig in.