Lay out two slices of the cinnamon swirl bread. Pile a quarter of the grated cheese onto each slice of bread. Layer the apple slices onto the cheese. Top with the remaining cheese. Close the sandwiches with the remaining two slices of bread. Spread a quarter of the softened butter onto the top of each sandwich.

Heat a skillet on medium low heat. Add one of the sandwiches, butter-side-down. Cook, covered, until the cheese begins to melt together and the bottom slice of bread is toasted, about 3-4 minutes.

Use a spatula to remove the sandwich from the pan. Add half of the remaining butter, and place the sandwich back in the pan, so that the unbuttered side is now down. Cook, uncovered, until the cheese is oozing from the sides of the sandwich and the bottom slice of bread is browned.

Cook remaining sandwich. Slice the sandwiches diagonally and serve dusted with cinnamon sugar is desired.