Preheat the oven to 325°F. Line a springform pan with parchment paper. In a bowl, mix graham cracker crumbs, sugar, cinnamon, and melted butter until combined. Press the mixture into the bottom of the pan and bake for 8 minutes. Let cool.
In a bowl, toss diced apples with sugar, cinnamon, nutmeg, and lemon juice. Let sit while preparing the cheesecake filling.
In a large bowl, beat cream cheese and sugar until smooth. Add eggs one at a time, mixing well after each addition. Stir in vanilla extract and sour cream until fully combined.
Pour the cheesecake filling over the cooled crust. Spread the apple mixture evenly on top. In another bowl, mix flour, oats, brown sugar, and cinnamon. Cut in the cold butter with a fork until crumbly, then sprinkle over the apples. Bake for 45-50 minutes until the center is set. Allow to cool completely before refrigerating for at least 4 hours.