In a medium bowl, mix the graham cracker crumbs and sugar together. Pour in the melted butter and stir until the crumbs are evenly moistened. Press firmly into the bottom of a 9-inch springform pan. Use the bottom of a measuring cup to get it even and compact. Place in the freezer while you prepare the filling.

In a large mixing bowl, beat the cream cheese and sugar on medium speed until creamy and smooth, about 2 minutes. Add eggs one at a time, beating after each addition. Mix in the vanilla, sour cream, and heavy cream until combined. Do not overmix, as this can cause cracks later.

Pour the filling over the prepared crust. Wrap the outside of the springform pan with foil to prevent leaks, then place it in a larger baking pan. Pour hot water into the larger pan until it reaches halfway up the sides of the springform pan. Bake at 325°F for 60 to 65 minutes, until the center is set but still slightly jiggly. Turn off the oven, crack the door, and let the cheesecake cool inside for 1 hour.

Remove the cheesecake from the water bath, discard the foil, and let it cool to room temperature. Cover and refrigerate for at least 4 hours or overnight. This chilling time helps the flavors deepen and the texture set perfectly.

In a medium saucepan, melt butter over medium heat. Add the apples, brown sugar, cinnamon, and nutmeg. Cook, stirring gently, until apples are tender but not mushy, about 6 to 8 minutes. If you prefer a thicker topping, stir in the cornstarch mixture and cook for 1 more minute. Let cool slightly before topping the cheesecake.

Spoon the cooled apple mixture over the chilled cheesecake. Drizzle generously with caramel sauce just before serving. Slice with a sharp knife, wiping between cuts for clean slices.