Preheat the oven to 325°F (160°C).
In a mixing bowl, combine the graham cracker crumbs and granulated sugar. Stir in the melted butter until the mixture resembles wet sand. Press the mixture firmly into the bottom of the springform pan to form a crust.
In a large mixing bowl, beat the softened cream cheese until smooth. Add the granulated sugar and vanilla extract, mixing until well combined.
Add the eggs, one at a time, mixing well after each addition. Then, stir in the sour cream and ground cinnamon until smooth.
Pour the cheesecake batter over the prepared crust, smoothing the top with a spatula.
Bake in the preheated oven for about 60 minutes, or until the edges are set and the center slightly jiggles. Turn off the oven and leave the cheesecake inside for 1 hour to cool slowly.
While the cheesecake cools, prepare the apple topping. In a skillet over medium heat, melt the butter. Add the sliced apples, brown sugar, lemon juice, and ground cinnamon. Cook for about 5-7 minutes, until the apples are tender but not mushy.
Once the cheesecake has cooled to room temperature, refrigerate it for at least 4 hours, preferably overnight.
Before serving, top the cheesecake with the sautéed apples and drizzle caramel sauce over it.