Prepare the apple filling by peeling, coring, and slicing the apples, then cooking them with butter, brown sugar, cinnamon, and lemon juice until tender.

Make the graham cracker crust by crushing the graham crackers and mixing them with sugar, cinnamon, and melted butter before pressing into a springform pan.

Prepare the cheesecake filling by beating cream cheese with sugar, vanilla, and salt, then mixing in sour cream, eggs, and cornstarch.

Create the crumble topping by combining oats, flour, brown sugar, cinnamon, and melted butter until crumbly.

Assemble the cheesecake by layering half the cheesecake mixture, the apple filling, then the remaining cheesecake mixture, topped with crumble.

Bake in a preheated oven at 150°C (300°F) for about 60 minutes, then cool gradually in the oven.

Chill the cheesecake in the refrigerator for at least 4 hours before serving.

Serve with optional caramel sauce or powdered sugar.