Preheat the oven to 350°F (175°C) and line a 9x13-inch baking pan with parchment paper, leaving an overhang on the sides.

In a medium bowl, combine graham cracker crumbs, granulated sugar, melted unsalted butter, and a pinch of salt. Press this mixture firmly and evenly into the bottom of the prepared pan.

Bake the crust for 8-10 minutes to help it set.

While the crust bakes, beat softened cream cheese and ¾ cup granulated sugar in a large bowl until smooth, then add eggs one at a time, mixing well after each addition.

Stir in sour cream, vanilla extract, and all-purpose flour until just combined, being careful not to overmix. Pour this cheesecake mixture evenly over the pre-baked crust.

Peel, core, and slice the apples, then toss them with lemon juice to prevent browning.

Melt 2 tablespoons unsalted butter in a large skillet over medium heat, then add the sliced apples, brown sugar, ground cinnamon, optional nutmeg, and a pinch of salt.

Cook the apples for 5-7 minutes until tender-crisp, then spoon them evenly over the cheesecake layer in the pan.

Bake the bars in the preheated oven for 45-55 minutes, until the edges are set but the center still jiggles slightly.

Turn off the oven and leave the bars inside with the door ajar for 15 minutes to prevent cracking, then remove and cool completely on a wire rack at room temperature.

Refrigerate the cooled bars for at least 4 hours, or preferably overnight, until firm.

Once chilled, warm the caramel sauce slightly for easier drizzling and generously apply it over the bars before lifting them out of the pan using the parchment overhang, cutting into squares, and serving.