Preheat your oven to 325°F (160°C). Grease the springform pan and set it aside.
In a mixing bowl, combine graham cracker crumbs, melted butter, and granulated sugar. Stir until well combined.
Press the mixture evenly into the bottom of the prepared springform pan to form the crust. Bake in the preheated oven for 10 minutes, then remove and let cool.
In another bowl, beat the softened cream cheese with an electric mixer until smooth. Gradually add the granulated sugar and vanilla extract, mixing until well combined.
Incorporate the eggs one at a time, mixing well after each addition. Add the sour cream and caramel sauce, mixing until smooth and creamy.
Pour the cheesecake filling over the cooled crust and spread it evenly. Bake for 50 minutes or until the center is set but slightly jiggly.
While the cheesecake is baking, prepare the apple topping. In a saucepan, melt the butter over medium heat, then add the sliced apples, brown sugar, and cinnamon. Cook for 5-7 minutes until apples are tender but still hold their shape. Remove from heat and let cool.
Once the cheesecake is done baking, remove it from the oven and allow it to cool at room temperature for about 15 minutes. Then, chill it in the refrigerator for at least 4 hours or overnight.
Before serving, top the cheesecake with the spiced apples and drizzle with additional caramel sauce.