Preheat your oven to 325 degrees Fahrenheit and line a 9x13 baking dish with parchment paper.
In a bowl, mix graham cracker crumbs, melted butter, and sugar until combined. Press firmly into the bottom of the pan. Bake for 10 minutes and set aside.
In a saucepan over medium heat, cook apples with butter, brown sugar, cinnamon, nutmeg, and vanilla. Stir occasionally until apples are tender, about 8 to 10 minutes. Remove from heat.
In a large bowl, beat cream cheese and sugar until smooth. Add eggs one at a time, then vanilla, mixing until just combined.
Pour cheesecake filling over the crust and spread evenly. Spoon apples over the cheesecake layer.
Bake for 35 to 40 minutes, until the center is set but slightly jiggly.
Cool completely, then refrigerate for at least 2 hours. Drizzle with caramel sauce before slicing and serving.