In a small skillet heat 1 tablespoon of butter over medium heat. Add the onions and saute for 5 minutes. Add in the brown sugar, mix well, and continue to saute for 15 minutes or until the onions are caramelized. Remove from heat
Using the remaining butter, butter one side of each of the four slices of bread. Place two slices in a large skillet over medium heat. Divide the cheddar cheese slices, the apple slices, and finally the caramelized onions between the two sandwiches. Top with remaining slice of bread.
Heat for 3-5 minutes per side or until the bread is golden brown and the cheese is melted.