1Prepare the apple pie filling by combining apples, brown sugar, cinnamon, water, lemon juice, butter, and salt in a saucepan. Cook until softened, then add a cornstarch-water mixture to thicken.
2Make the crust by combining graham cracker crumbs, granulated sugar, brown sugar, and melted butter. Press into a greased 9-inch springform pan.
3Create the crumble topping by mixing flour, brown sugar, oats, cinnamon, salt, and melted butter.
4In a large bowl, beat softened cream cheese until smooth and creamy. Add sugar, sour cream, vanilla, and salt; mix well.
5Add eggs one at a time, mixing until just combined.
6Pour cheesecake filling into the prepared pan. Top with apple filling and crumble topping.
7Bake at 325°F (160°C) for 60-75 minutes, or until edges are puffed and the center is jiggly. Cool completely and refrigerate for at least 6 hours or overnight.