Preheat your oven to 325°F (160°C). Combine graham cracker crumbs, melted unsalted butter, and granulated sugar until the mix resembles wet sand. Press into the bottom of a 9-inch springform pan and bake for 10 minutes. Cool completely.

Beat softened cream cheese on medium speed until smooth, about 2-3 minutes. Gradually add granulated sugar and vanilla extract, blending thoroughly. Incorporate eggs one at a time, mixing gently. Fold in the sour cream.

In a saucepan, combine peeled and diced apples with brown sugar, cinnamon, lemon juice, and water. Cook for 5-7 minutes until softened. Mix cornstarch with cold water, stir into apple mixture, and cook for 1 minute until slightly thickened. Let cool.

Mix all-purpose flour, brown sugar, and cinnamon. Add cold cubed unsalted butter and combine until crumbly. This will form the topping for the cheesecake.

Pour the cheesecake filling over the crust. Layer the apple filling on top, then sprinkle the crumble topping over the apples. Bake for 55-65 minutes until edges are set and the center jiggles slightly.

Turn off the oven and leave the cheesecake inside for about an hour to cool, then refrigerate for at least 4 hours or overnight to chill.

Once chilled, remove the cheesecake from the springform pan, slice into portions, and serve chilled with optional caramel sauce or whipped cream.