Preheat oven to 350°F. Par bake (blind bake) the crust by lining it with foil and pie weights. Bake for about 20 minutes. Remove the foil and bake until the bottom crust is set, but not coloring at all.
In a skillet, heat the apples, butter, brown sugar, cinnamon and salt until the apples are tender. In a small bowl combine the cornstarch and water. If your apples have a lot of liquid use just 2 tablespoon of water. If they are drier, add the remaining 2 tablespoons water. Stir over medium heat until the apple juices thicken and the cornstarch no longer looks cloudy. Allow the apples to cool while you prepare the pumpkin filling.
Whisk together the pumpkin, brown sugar, salt, cinnamon, ginger, nutmeg, all-spice, eggs, sour cream and vanilla. Turn down the oven to 325°F.
Put the apples in the par baked pie shell. Pour in the pumpkin over the apples. If there are any large bubbles, pop them with a fork. Bake the caramel apple pumpkin pie for about 1 hour, but check after 45 minutes to gauge how quickly it is setting up. You want to take it out when the pumpkin is set and just puffing ever so slightly. You don't want it to be liquid in the middle, but you also don't want the pie to soufflé or it will crack.
Set it to cool on a rack. The caramel apple pumpkin pie cuts better when chilled and I prefer the flavor. You can try it chilled or at room temperature.