Make the crust:
Preheat your oven to 350°F (175°C). In a mixing bowl, combine the graham cracker crumbs, melted butter, and granulated sugar. Mix well until the texture resembles wet sand. Press this mixture firmly into the bottom of a 9-inch springform pan to form an even crust. Set aside while you prepare the remaining layers.
Make the apple filling:
In a medium skillet over medium heat, melt 2 tablespoons of the butter. Add the thinly sliced apples, brown sugar, cinnamon, and nutmeg. Cook, stirring occasionally, until the apples are just softened and coated in the syrupy mixture, about 5-7 minutes. Remove from heat and let cool slightly.
Make the Cheesecake Filling:
In a large mixing bowl, beat together the softened cream cheese, granulated sugar, and vanilla extract until smooth and creamy. Add the eggs, one at a time, beating on low speed just until each egg is incorporated. Be careful not to overmix, as this can cause the cheesecake to crumble. Pour half of the cheesecake filling over the prepared springform pan crust.
Apple Layer:
Spread half of the cooled apple filling evenly over the cheesecake layer. Pour the remaining cheesecake mixture on top and smooth it out. Finish by adding the remaining apple filling on top.
Add the Crisp Topping:
In a separate bowl, mix together the flour, oats, brown sugar, and cinnamon. Cut in the cold, cubed butter using a pastry cutter or your fingers until the mixture becomes crumbly and resembles coarse crumbs. Sprinkle this mixture generously on top of the cheesecake.
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