Prepare the crust: Combine graham cracker crumbs, sugar, and melted butter. Press into the bottom of the springform pan.
Make the cheesecake filling: Beat cream cheese and sugar until smooth. Add eggs, vanilla, and sour cream, mixing well.
Prepare the apples: Toss apple slices with sugar, cinnamon, nutmeg, and lemon juice. Set aside.
Make the crumble topping: Mix oats, brown sugar, and flour. Add cold butter and rub until crumbly.
Assemble the cheesecake: Pour cheesecake mixture over the crust. Layer spiced apples on top, followed by the crumble topping.
Bake: Preheat the oven to 325°F (163°C). Bake for 50-60 minutes or until the cheesecake is firm and golden.
Make the caramel sauce: In a saucepan, melt brown sugar and butter. Stir in heavy cream and vanilla, cooking until smooth and thickened.
Cool and serve: Let cheesecake cool in the pan, refrigerate for at least 2 hours. Drizzle with caramel sauce before serving.