Preheat oven to 325°F (163°C). Lightly grease a 9-inch springform pan.
In a medium bowl, mix graham cracker crumbs, sugar, and melted butter. Press mixture into the bottom of the pan and slightly up the sides. Bake for 10 minutes, then set aside to cool.
In a large bowl, beat cream cheese and sugar until smooth. Add eggs one at a time, beating well after each addition. Mix in vanilla and sour cream.
Pour the cheesecake filling into the crust. Bake for 55-60 minutes, or until the center is set but slightly jiggly.
Turn off the oven, crack the door, and let the cheesecake cool for 1 hour. Then transfer to the fridge to chill for at least 4 hours or overnight.
While the cheesecake chills, prepare the apple topping. In a skillet, melt butter over medium heat. Add apples, cinnamon, and brown sugar. Cook for 5-7 minutes until apples are tender. Let cool.
Before serving, spoon the apple topping over the chilled cheesecake and drizzle with caramel sauce.