Prepare Apple Filling: In a saucepan over medium heat, melt 2 tablespoons of butter, then add peeled and sliced medium apples along with ¼ cup of brown sugar, 1 teaspoon of cinnamon, and 1 tablespoon of lemon juice. Cook for about 8-10 minutes, stirring occasionally until the apples are fork-tender. To thicken, create a cornstarch slurry with 1 tablespoon of cornstarch mixed with 2 tablespoons of water. Stir this into the apple mixture, cooking for an additional minute until thickened, then set aside to cool.

Make Crust: Preheat your oven to 350°F (175°C) while you prepare the crust. In a medium bowl, combine 1 ½ cups of graham cracker crumbs, ¼ cup of granulated sugar, and 1 teaspoon of cinnamon. Pour in ½ cup of melted unsalted butter, mixing until the crumbs are evenly moistened. Firmly press this mixture into the bottom of a 9-inch springform pan. Bake for 8-10 minutes until golden brown, then let it cool.

Make Cheesecake Filling: In a large mixing bowl, use an electric mixer to beat 24 ounces of room-temperature cream cheese until smooth and creamy. Gradually blend in ¾ cup of granulated sugar, followed by 3 large eggs, one at a time, mixing thoroughly after each addition. Add 1 cup of sour cream, 2 tablespoons of cornstarch, and 1 teaspoon of vanilla extract, mixing until fully combined and silky, then set aside.

Assemble Cheesecake: Pour half of the cheesecake filling over the cooled crust, layer the apple filling evenly on top, and pour the remaining cheesecake batter over the apples. Mix together ½ cup rolled oats, ¼ cup flour, and ¼ cup melted butter to create the crumble topping, then sprinkle over the cheesecake.

Bake: Lower the oven temperature to 325°F (160°C) and carefully place the cheesecake in the preheated oven. Bake for 50-60 minutes until the edges are set and the center jiggles slightly.

Cool and Chill: Turn off the oven and leave the cheesecake inside with the door ajar for 1 hour. After an hour, remove it from the oven and let it cool completely at room temperature. Once cooled, cover it and refrigerate for at least 5 hours or overnight.

Serve: Slice into portions and drizzle warm caramel sauce over each slice. Pair with whipped cream or vanilla ice cream if desired.