Spread one side of each slice of bread with the butter, dividing it equally. Place 2 slices on a cutting board, butter side down (a bit messy, yes), and layer 3 slices of cheese or sprinkle 2⁄3 cup of grated cheese on each slice of bread. If you are using more than one kind of cheese, divide the different kinds as you like between the sandwiches. Top the sandwiches with the remaining 2 slices of bread, butter side up.
Heat a large skillet, either a nonstick skillet or one that has been sprayed with nonstick cooking spray, over medium heat. Carefully place the sandwiches in the skillet, cover it, and cook the sandwiches until the bottoms start to turn golden brown, about 2 minutes. Uncover the skillet and, using a spatula, turn the sandwiches over (be careful if you've used grated cheese to make sure the filling stays put). Press down on the sandwiches a bit with the spatula, and cook them uncovered until the second side is golden brown and crisp, about 3 minutes. Turn the sandwiches one more time, season lightly with salt, and cook them until the bottom is fully golden brown and crispy, 1 to 2 minutes longer.
Transfer the sandwiches to the cutting board, let them sit for 1 minute so that the cheese firms back up a bit, then cut the sandwiches in half and serve.
Notes
What the Kids Can Do: Pick their favorite cheese, choose any add-ins they like, and layer up their sandwiches.