1. Preheat oven to 325°F (160°C). In a bowl, mix graham cracker crumbs, melted butter, and sugar. Press into the bottom and slightly up the sides of a 9-inch springform pan. Bake for 10 minutes and let cool.
2. In another bowl, beat cream cheese and sugar until smooth. Add eggs one at a time, mixing after each addition. Stir in vanilla extract. Pour the mixture into the crust.
3. Bake for 50-55 minutes or until the center is just set. Let cool completely before refrigerating for at least 4 hours.
4. For the apple topping, melt butter in a skillet over medium heat. Add apples, brown sugar, and cinnamon. Cook until tender, about 5 minutes. Let cool.
5. Before serving, top the cheesecake with cooked apples and drizzle with caramel sauce.