Preheat oven to 375 degrees. In a small saucepan, combine water and cornstarch. Over low heat, stir in brown sugar, butter, salt, cinnamon, and lemon juice. Bring to a boil, stirring frequently. Stir in apple and cook briefly for 5 minutes until apples start to soften just a little and cornstarch thickens the mixture.
In a medium bowl, combine pumpkin, egg, white sugar, salt, pumpkin pie spice, and evaporated milk.
In a prepared pie crust in a 9" deep dish pie plate, pour cooked apples evenly over bottom. Pour pumpkin filling evenly over apples and pat gently with spatula to remove any air pockets. Bake in a 375 degree oven for 40 minutes. Allow to cool at room temperature at least one hour before cutting and serving. Keep refrigerated. Enjoy!