Preheat the oven to 350 degrees and line a 8x8 baking dish with parchment paper.
In a medium bowl, mix together crushed graham crackers, oats, brown sugar, and melted butter.
Press crust into the bottom of the prepared baking dish. and bake for 5 minutes. Set aside to cool.
In the bowl of a stand mixer, beat together cream cheese, granulated sugar, brown sugar and sour cream until light and fluffy, about 2 minutes. Beat in eggs, vanilla, cinnamon, and nutmeg until combined.
Pour cheesecake filling into the cooled crust and set aside.
For the topping, combine flour, oats, brown sugar, cinnamon, and butter in a small bowl and stir with a fork until combined. Evenly cover the cheesecake filling with the chopped apple and then the streusel topping.
Top cheesecake filling with the apple crisp topping and bake for 45-50 minutes. Center will jiggle slightly. Remove from the oven and let cool for 15 minutes.
Place cheesecake in the fridge to chill for 8 hours or overnight.
Lift cheesecake out of the pan using the parchment paper. Slice into 12 bars and serve with a drizzle of caramel sauce.