Lightly butter one side of each slice of bread.

Melt 2 teaspoons of the remaining butter in a 10-inch nonstick skillet over medium-low heat. Place 2 slices of bread, buttered side down, in the skillet, top each slice with about 1/4 cup of blue cheese and several slices of apple, and place another slice of bread on top, buttered side up. Cook until the sandwiches are golden brown on the bottom, then carefully flip the sandwiches over and brown the other side. Transfer the sandwiches to a serving platter. Repeat the process with the remaining ingredients. Slice the sandwiches in half on the diagonal and serve.