Preheat your oven to 325F, line a springform pan with parchment paper.
Add the graham crackers to a food processor and blend until you have fine crumbs. Add sugar and melted butter and mix until everything is well combined.
Pour the graham cracker mixture into the springform pan and press firmly with a flat-bottomed object. Bake for 15 minutes and allow to cool completely while you work on the cheesecake filling.
In a large bowl, beat the cream cheese with a hand mixer until smooth. Add in the vanilla, sour cream, eggs, and sugar and beat until smooth. Now set aside while you work on the apple topping.
Peel and dice 2 large apples, add to a pan with lemon juice, brown sugar, cinnamon, and butter. Cook over medium heat for 5-7 minutes until you have tender caramelized apples. Set aside to cool.
In a small bowl, add the flour, sugar, cinnamon, and butter. Work the dry ingredients into the butter until you have coarse crumbs.
Pour the cheesecake filling over the baked crust, layer the caramelized apples on top, and top it off with the crumble. Bake for 1 hour and 30-40 minutes or until the center is set.
Turn off your oven and crack the door open, leaving the cheesecake to rest inside for an hour before refrigerating. Refrigerate for at least 4 hours before cutting into it (please refrigerate for a few hours; I was running out of time, so I only let it sit in the fridge for 2 hours, and the cheesecake wasn't fully firm).
