Preheat the oven to 350°F.
Start with the apple filling. Peel and thinly slice the apples. In a large skillet over medium-high heat, combine the apples, butter, brown sugar, and cinnamon. Sauté for about 3–4 minutes, just until the apples begin to soften.
In a small bowl, mix the cornstarch and water until smooth. Pour it into the apple mixture and stir until the sauce thickens. Remove from the heat and allow the apples to cool completely.
For the crust, crush the graham crackers into fine crumbs using a food processor. Combine the crumbs with the melted butter and mix well. Lightly spray a 9-inch springform pan with nonstick cooking spray, then firmly press the graham cracker mixture into the bottom of the pan. Bake for 7–8 minutes, then remove and allow it to cool.
Reduce the oven temperature to 300°F.
For the cheesecake filling, beat the softened cream cheese, sugar, and vanilla until smooth and creamy. Add the sour cream and heavy whipping cream and mix just until combined, scraping down the sides of the bowl as needed.
Crack the eggs into a separate bowl and gently mix them by hand. Slowly add the eggs to the cheesecake mixture, mixing only until incorporated. Avoid overmixing once the eggs are added.
Pour half of the cheesecake batter over the prepared crust. Spoon the cooled cinnamon apples evenly over the batter, then carefully cover them with the remaining cheesecake mixture.
To make the crumble, combine the flour, sugar, and brown sugar. Grate the frozen butter into the mixture—or cut it into very small pieces—and work everything together until you have a chunky, sandy crumble. Sprinkle evenly over the cheesecake.
If you’re worried about your springform pan leaking, wrap the outside with aluminum foil. Bake at 300°F for approximately 1 hour, or until the edges are set and the center still has a slight jiggle.
Remove the cheesecake from the oven and allow it to cool in the pan for about 1 hour. Once cooled, carefully remove it from the springform pan and refrigerate for 8–24 hours, preferably overnight.
When you’re ready to serve, drizzle generously with caramel sauce.