Preheat the oven to 325°F (163°C).
In a bowl, combine graham cracker crumbs, melted butter, and sugar. Press the mixture firmly into the bottom of a 9-inch springform pan. Bake for 10 minutes, then set aside to cool.
In a large mixing bowl, beat cream cheese and sugar until smooth. Add eggs one at a time, mixing well after each addition. Mix in vanilla extract and sour cream until combined.
Pour the filling over the cooled crust and smooth the top.
Place the springform pan on a baking sheet and bake for 50-60 minutes, or until the center is slightly jiggly but set around the edges.
Turn off the oven and crack the door open. Let the cheesecake cool in the oven for 1 hour to prevent cracking.
In a saucepan, melt butter over medium heat. Add diced apples, brown sugar, and cinnamon. Cook until the apples are soft, about 5-7 minutes. Stir in the cornstarch slurry and cook until thickened. Remove from heat and let cool.
Once the cheesecake has cooled completely, spoon the apple topping over the top. Drizzle with caramel sauce.
Refrigerate the cheesecake for at least 4 hours or overnight. Remove from the springform pan, slice, and serve chilled.