Prepare the Graham Cracker Crust: In a medium bowl, combine graham cracker crumbs, melted butter, and sugar. Press the mixture firmly into the bottom of a 9×13 inch baking pan lined with parchment paper.
Make the Cheesecake Filling: In a large bowl, beat the softened cream cheese and sugar until smooth and creamy. Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract and sour cream until just combined. Do not overmix.
Prepare the Caramel Apple Topping: In a large skillet, melt the butter over medium heat. Add the diced apples and sugar, and cook until the apples are tender and slightly caramelized, about 8-10 minutes. Stir in the cinnamon and nutmeg.
Assemble and Bake: Pour the cheesecake filling over the graham cracker crust. Spoon the caramel apple mixture evenly over the cheesecake filling. Drizzle the caramel sauce over the top. Bake in a preheated oven at 350°F (175°C) for 30-35 minutes, or until the edges are set and the center is slightly jiggly.
Cool and Chill: Let the cheesecake bars cool completely in the pan. Cover and refrigerate for at least 4 hours, or preferably overnight, before slicing and serving.
