Butter one side of each bread slice. Place 4 bread slices buttered side down on a work surface and top with half of the cheese, distributing evenly. Cover with an even layer of red pepper strips and top with the remaining cheese. Close the sandwiches with the remaining bread slices buttered side up.
Heat a large griddle over low heat. Working in batches if necessary, add the sandwiches to the pan and cook for 3 minutes. Using a wide metal spatula, flip the sandwiches, then cook for 3 minutes on the second side. Continue flipping, cooking for about 3 minutes more on each side, until the bread is crisped and the cheese is melted. Cut each sandwich into 6 bite-size pieces.