Preheat your oven to 325°F (160°C). In a medium bowl, combine graham cracker crumbs, melted butter, and sugar until well-blended. Press this mixture firmly into the bottom of a 9-inch springform pan, creating an even layer. Bake for 10 minutes until fragrant and lightly golden, then allow to cool completely.

In a large mixing bowl, beat softened cream cheese with a hand mixer until smooth and creamy. Gradually add sugar and vanilla extract, mixing well until combined. Then, add eggs one at a time, blending on low speed. Gently fold in sour cream until fully incorporated.

Pour the cheesecake filling into the cooled crust, smoothing the top evenly.

In a medium saucepan, combine diced apples, brown sugar, cinnamon, lemon juice, and water. Cook for 5–7 minutes, stirring frequently, until slightly softened. Mix cornstarch with water, then stir into apples and cook for an additional 2–3 minutes until thickened.

In a mixing bowl, combine flour, brown sugar, and cinnamon. Cut in cold butter until crumbly.

Spoon the warm apple filling over the cheesecake layer, spreading it evenly. Sprinkle the crumble topping over the apple mixture. Bake for 55–65 minutes until the center is slightly jiggly but set.

Turn off the oven and crack open the door, allowing the cheesecake to cool gradually for 1 hour. Afterward, transfer to the refrigerator and let chill for at least 4 hours, or overnight.