Prepare the crust: Mix graham cracker crumbs, sugar, and melted butter. Press mixture into the base of the springform pan.
Make the cheesecake filling: Beat the cream cheese and sugar until smooth. Add eggs, vanilla, and sour cream; mix until well combined.
Prepare the apples: Toss apple slices with sugar, cinnamon, nutmeg, and lemon juice. Set aside.
Make the crumble topping: In a bowl, mix oats, brown sugar, and flour. Add cold butter and rub together until crumbly.
Assemble the cheesecake: Pour cheesecake mixture over the crust. Layer spiced apples on top. Sprinkle crumble topping evenly over apples.
Bake: Preheat the oven to 325°F (163°C). Bake for 50-60 minutes until cheesecake is set and golden.
Cool and serve: Let it cool in the pan, then refrigerate for at least 2 hours. Serve chilled.