Spread the butter on one side of each bread slice.
Using a large hole grater, grate the cheddar cheese onto a side plate. Note that grating the cheese too finely will cause it to melt too quickly.
Take two bread slices and face them buttered-side down. Spread the cheese on the unbuttered side.
Season the cheese with salt and pepper to taste.
For both sandwiches, cover the cheese with the second slice of bread, buttered-side facing up.
Heat the nonstick frying pan or griddle to hot but not smoking. Lay the sandwiches on the pan using a flat spatula. As you do, you should hear a sizzle.
Using the spatula, gently press the sandwiches down. Allow them to cook for a few minutes before flipping them over and repeating on the other side.
Once the cheese melts and the bread is golden brown, remove the toasties from the pan. Cut each one in half diagonally.
Serve hot, and enjoy!