Preheat the oven to 325°F (160°C).

In a mixing bowl, combine the graham cracker crumbs, melted butter, and sugar. Mix until well combined.

Press the crumb mixture evenly into the bottom of a 9-inch springform pan. Bake for 10 minutes, then remove and set aside to cool.

In a large mixing bowl, beat the softened cream cheese with an electric mixer until smooth and creamy.

Gradually add the granulated sugar and vanilla extract, mixing until well incorporated.

Add the eggs one at a time, mixing on low speed after each addition until just combined. Avoid overmixing.

Stir in the sour cream, ground cinnamon, and nutmeg until smooth. Pour the filling over the cooled crust in the springform pan.

Bake the cheesecake for about 55-60 minutes, or until set but slightly jiggly in the center. Turn off the oven, crack the door, and let the cheesecake cool in the oven for an hour.

In a saucepan over medium heat, melt the butter for the apple topping. Add the diced apples, brown sugar, vanilla, and cinnamon. Cook for about 5-7 minutes, stirring occasionally, until apples are tender. Set aside to cool.

For the caramel sauce, combine the granulated sugar and butter in a saucepan over medium heat. Stir constantly until the sugar is melted and the mixture is bubbly.

Slowly add the heavy cream while continuing to stir, then remove from heat and stir in the vanilla extract. Let cool slightly.

Once the cheesecake has cooled, top it with the sautéed apples and drizzle with caramel sauce. Refrigerate for at least 4 hours, preferably overnight, before serving.

Carefully remove the sides of the springform pan before slicing and serving. Drizzle with additional caramel sauce if desired.