1.Preheat the oven to 325°F (165°C).

1. In a medium bowl, combine graham cracker crumbs and melted butter.
2. Press the mixture firmly into the bottom of a 9-inch springform pan.
3. Bake for 8-10 minutes, or until lightly golden. Let cool completely.
4. In a large bowl, beat cream cheese until smooth.
5. Gradually add granulated sugar, beating until light and fluffy.
6. Beat in sour cream and vanilla extract.
7. Add eggs one at a time, beating until just combined after each addition. Be careful not to overmix.
8. In a medium bowl, combine sliced apples, granulated sugar, flour, cinnamon, and nutmeg. Toss to coat evenly.
9. Pour the cheesecake filling into the cooled crust.
10. Top with the apple mixture.
11. In a medium bowl, whisk together flour, granulated sugar, brown sugar, and cinnamon.
12. Cut in cold butter using a pastry blender or your fingers until the mixture resembles coarse crumbs.
13. Sprinkle the crumble topping evenly over the apple layer.
14. Bake in the preheated oven for 50-60 minutes, or until the center is set and the topping is golden brown.
15. Let the cheesecake cool to room temperature, then refrigerate for at least 4 hours or overnight before serving.