Step 1: Prepare the Graham Cracker Crust
Preheat your oven to 325°F (165°C). Lightly grease a 9-inch springform pan and line the bottom with parchment paper for easy removal. In a medium mixing bowl, combine the graham cracker crumbs, melted butter, and granulated sugar. Mix until the texture resembles wet sand. Press the mixture firmly into the bottom of the prepared pan, using the bottom of a glass or measuring cup to create an even layer. Bake the crust for 10 minutes, then set it aside to cool while you prepare the other layers.

Step 2: Make the Cheesecake Filling
In a large mixing bowl, beat the cream cheese with a hand mixer or stand mixer fitted with the paddle attachment until smooth and creamy. Add the granulated sugar and continue to beat until fully incorporated. Mix in the sour cream and vanilla extract. Add the eggs, one at a time, mixing on low speed after each addition just until combined. Avoid overmixing, as this can cause the cheesecake to crack. Pour the cheesecake batter over the cooled crust, spreading it out evenly.

Step 3: Prepare the Apple Filling
In a separate bowl, toss the sliced apples with granulated sugar, cinnamon, nutmeg, and flour until the apples are evenly coated. Arrange the apple slices in a single layer on top of the cheesecake filling. It’s okay if they overlap slightly, but try to create an even distribution for balanced flavor.

Step 4: Make the Crumble Topping
In another bowl, combine the flour, oats, brown sugar, cinnamon, and salt. Add the chilled, cubed butter, and use your fingers or a pastry cutter to mix until the texture resembles coarse crumbs. Sprinkle the crumble topping evenly over the apples.

Step 5: Bake the Cheesecake
Place the springform pan on a baking sheet to catch any drips. Bake the cheesecake in the preheated oven for 60-70 minutes, or until the edges are set and the center is slightly jiggly. If the top is browning too quickly, tent the pan loosely with aluminum foil.

Step 6: Cool the Cheesecake
Once baked, remove the cheesecake from the oven and let it cool in the pan for 1 hour at room temperature. Then, refrigerate it for at least 3 hours or overnight to allow it to fully set.

Step 7: Serve
Remove the sides of the springform pan and transfer the cheesecake to a serving plate. Drizzle with caramel sauce, add a dollop of whipped cream, or sprinkle with chopped pecans for an extra-special presentation. Slice and enjoy!