Preheat your oven to 325°F (160°C). Line a 9x9-inch baking dish with parchment paper, leaving some hanging over the sides for easy removal later.
In a medium bowl, combine the graham cracker crumbs and melted butter, mixing until well combined. Press this mixture firmly into the bottom of the prepared baking dish to create an even crust. Bake for 10 minutes and then remove from the oven to cool slightly.
In a large mixing bowl, beat the softened cream cheese with an electric mixer on medium speed until smooth and creamy, about 1-2 minutes.
Gradually add the granulated sugar, beating until well incorporated. Then, mix in the vanilla extract, followed by the eggs, one at a time, making sure to mix well after each addition.
In a separate bowl, toss the chopped apples with cinnamon, nutmeg, and a pinch of salt. Fold the apple mixture into the cream cheese batter gently.
Pour the apple cheesecake filling over the prepared crust in the baking dish and spread it evenly. Drizzle the caramel sauce over the top of the filling, creating a marbled effect by using a knife or a toothpick to swirl it gently.
Bake in the preheated oven for 30-35 minutes, or until the edges are set, and the center has a slight jiggle. Remove from oven and allow to cool at room temperature, then refrigerate for at least 3 hours, or until fully chilled and firm.
Once chilled, lift the bars out of the baking dish using the parchment paper overhang. Cut into squares and drizzle additional caramel sauce on top before serving.
Notes
For an elegant touch, garnish with thin apple slices and a sprinkle of cinnamon.