Preheat your oven to 350°F (175°C).

In a large bowl, combine the graham cracker crumbs, melted butter, and granulated sugar. Press this mixture firmly into the bottom of a 9-inch springform pan.

Bake for 10 minutes and then set aside to cool.

In another large bowl, beat the softened cream cheese until smooth.

Gradually add in the granulated sugar and vanilla extract, mixing until well combined.

Incorporate the eggs one at a time, mixing on low speed, and scrape down the sides of the bowl after each addition.

Finally, fold in the sour cream until everything is well blended.

In a medium bowl, toss the diced apples with brown sugar, cinnamon, cornstarch, water, and lemon juice. Set this mixture aside.

Pour the cheesecake filling over the cooled crust and smooth the top.

Spoon the apple mixture over the cheesecake layer.

For the crumble topping, mix together the all-purpose flour, brown sugar, and cinnamon in a medium bowl.

Cut in the cold butter until the mixture resembles coarse crumbs, then sprinkle it over the apple layer.

Bake for about 60-70 minutes, or until the center is set but slightly wobbly.

Let it cool at room temperature for about an hour, and then refrigerate for at least four hours before serving.