Preheat your oven to 325°F (160°C). In a mixing bowl, combine graham cracker crumbs, melted unsalted butter, and granulated sugar until the mixture resembles wet sand. Press this mixture firmly into the bottom of a 9-inch springform pan to create an even layer. Bake for 10 minutes, or until lightly golden, then remove from the oven and let it cool while you prepare the filling.

In a large mixing bowl, beat the softened cream cheese with an electric mixer on medium speed until smooth, about 2 minutes. Gradually add granulated sugar and vanilla extract, mixing well. Incorporate the eggs one at a time, mixing gently after each addition. Finally, fold in the sour cream until completely integrated. Pour this rich cheesecake filling over the cooled crust, spreading it evenly.

In a medium saucepan over medium heat, combine the diced apples, brown sugar, cinnamon, lemon juice, and a splash of water. Cook for about 5-7 minutes, stirring occasionally, until the apples begin to soften and the mixture slightly thickens. Remove from heat and add a cornstarch slurry by mixing cornstarch with a bit of water before folding it in.

In another mixing bowl, combine all-purpose flour, brown sugar, and cinnamon. Cut in the cold unsalted butter using a pastry cutter or your fingertips until the mixture resembles coarse crumbs. Set aside while you complete the assembly.

Layer the slightly cooled apple filling gently over the cheesecake batter, spreading it out evenly. Sprinkle the crumble topping generously over the apple layer, ensuring it covers the filling entirely. Bake in the preheated oven for 55-65 minutes or until the edges are set and the center remains slightly jiggly.

Once baked, turn off the oven and crack the door open, allowing the cheesecake to cool in the oven for about 1 hour. Afterward, transfer the cheesecake to the refrigerator and chill for at least 4 hours, preferably overnight, to set the flavors and textures beautifully.