Cook the apples:
In a saucepan over medium heat, combine the sliced apples, granulated sugar, brown sugar, cinnamon, nutmeg, cornstarch, lemon juice, and water. Stir frequently and cook for about 8-10 minutes, until the apples are softened and the mixture has thickened. Let it cool.
Prepare the Cheesecake Filling:
Beat the cream cheese:
In a large bowl, beat the softened cream cheese and sugar until smooth and creamy. Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract and sour cream.
Swirl cinnamon (optional):
If you like, you can mix 1/2 teaspoon of cinnamon into the cheesecake batter for a slight cinnamon swirl.
Assemble the Cheesecake:
Layer the apple pie filling:
Pour half of the cheesecake filling over the graham cracker crust. Gently spoon half of the apple pie filling on top of the cheesecake batter.
Add the second layer:
Pour the remaining cheesecake filling over the apples and then spoon the remaining apple pie filling on top. You can swirl the apple mixture lightly into the cheesecake batter using a knife or leave it as is.
Bake:
Bake the cheesecake:
Wrap the bottom of the springform pan with aluminum foil to prevent water from leaking in. Place the cheesecake in a large roasting pan and add hot water to the pan, about halfway up the sides of the springform pan (water bath method). Bake for 60-70 minutes, or until the center is just set and slightly jiggly.
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