Spread 1 tablespoon of cranberry sauce on each of the bread slices, so it covers one side. Layer the cheddar and apple slices over the cranberry sauce on two of the bread slices. Place the other two bread slices, sauce side down, over the filling.
Melt 2 tablespoons of butter in a large skillet over medium-low heat. Carefully place sandwiches in the skillet, and gently press down on them with the back of a spatula. Cook until the first side is golden brown, about 5 minutes. (While the grilled cheeses cook, spread 1 tablespoon of butter over the top of each sandwich.)
Flip the sandwiches over and cook for an additional 3-5 minutes, until the cheese is melted and the bread is toasted. Transfer to a plate and serve warm.