Combine the brown sugar, cornstarch, 1/2 tsp of cinnamon and 1/4 tsp of salt in a 2-quart saucepan. Stir in the water and butter. Cook, over medium heat, stirring constantly, until the mixture comes to a boil. Carefully add the apple slices and cook for another 4 minutes. Remove from the heat and set aside. Combine the egg, sugar, pumpkin, 1/4 ts of salt, spices, and evaporated milk in a bowl. Beat until well blended using a rotary or electric mixer set on low speed. Pour the apple mixture into the unbaked pie shell and then spoon an even layer of the pumpkin mixture over the apple mixture. Bake in a preheated 425 degree F oven for 10 minutes then reduce the oven temperature to 375 degrees F and bake another 40 minutes or until the filling is set around the edge. Cool on a wire rack.