Prepare the Crust:
Preheat oven to 325°F (163°C).
Mix crushed graham crackers, melted butter, and sugar until combined.
Press into the bottom of a springform pan and bake for 10-12 minutes. Let cool.
Make the Cheesecake Filling:
In a large bowl, beat cream cheese until smooth.
Add sugar, cornflour, lemon zest, and vanilla extract, mixing until combined.
Add eggs one at a time, mixing gently.
Fold in sour cream until the batter is smooth.
Prepare the Apple Filling:
In a pan, melt butter over medium heat.
Add apples, brown sugar, cinnamon, nutmeg, and vanilla extract.
Cook for 5-7 minutes, until apples are soft but still hold their shape.
Make the Crumble Topping:
In a bowl, mix flour, oats, brown sugar, cinnamon, and salt.
Cut in cold butter until the mixture forms coarse crumbs.
Assemble the Cheesecake:
Pour half of the cheesecake batter over the cooled crust.
Layer apple filling over the batter.
Pour the remaining cheesecake batter on top.
Sprinkle with crumble topping evenly.
Bake the Cheesecake:
Reduce oven temperature to 300°F (150°C).
Place the springform pan in a water bath (wrap the pan in foil and set it in a larger dish filled with hot water).
Bake for 60-75 minutes, until the center is slightly jiggly but the edges are set.
Turn off the oven and let the cheesecake cool inside for 1 hour.
Refrigerate for at least 6 hours or overnight before serving.