Preheat your oven to 325°F (163°C). Grease a 9-inch springform pan with butter or non-stick spray.

Combine graham cracker crumbs, 1/4 cup granulated sugar, and melted butter in a mixing bowl until the mixture resembles wet sand. Press into the bottom of the greased pan. Bake for 10 minutes until golden and cool slightly.

Beat softened cream cheese on medium speed until smooth, about 2 minutes. Gradually add in 1 cup sugar, mix well, and then incorporate eggs one at a time, mixing on low. Add vanilla and sour cream until blended.

Pour the creamy filling over the cooled crust, smoothing the top. Create a water bath by placing the springform pan in a larger roasting pan, filling with hot water halfway up the sides.

Bake the cheesecake for 55-65 minutes. It should be slightly jiggly in the center. Turn off the oven, crack the door, and let it cool in the oven for about 1 hour.

After cooling, remove the cheesecake from the oven. Allow it to cool at room temperature for 30 minutes before refrigerating it for at least 4 hours or overnight.

Melt 2 tablespoons of unsalted butter in a skillet over medium heat. Add diced apples with brown sugar, cinnamon, and nutmeg. Cook until tender and syrupy, about 8 minutes, then set aside to cool.

Heat 1 cup of granulated sugar in a saucepan over medium heat, stirring constantly until it melts and turns amber. Add cubed butter and whisk in 1/2 cup heavy cream, being cautious of splatters. Allow it to boil for 1 minute, then stir in 1 teaspoon sea salt, and let cool.

Once the cheesecake has chilled, layer the sautéed apples over the top. Drizzle the salted caramel sauce over the apples before serving.