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