For the apple filling, melt the butter in a wide sauté pan over a medium heat and add the diced apples. Sprinkle with the demerara sugar and cinnamon and toss. Reduce the heat to low and cook the apples until they exude water; raise the heat to high and, stirring frequently, let the excess juices reduce. Test the apples for doneness: if they still seem hard, turn the hea