Preheat your oven to 350°F. Line a 9x13-inch baking dish with parchment paper, leaving a bit of overhang on the sides for easy removal later. Set aside.
Make the crust: In the bowl of a stand mixer, combine the softened butter, brown sugar, and flour. Mix on medium speed until the mixture forms coarse crumbs.
Transfer the crust mixture to the prepared pan and press it firmly and evenly into the bottom to form a solid layer.
Bake the crust for 14-16 minutes, or until lightly golden around the edges. Remove from the oven and set aside to cool slightly while you prepare the filling.
Prepare the cheesecake layer: In a clean stand mixer bowl, beat the cream cheese on medium-high speed until smooth and creamy, about 1 minute. Add the sugar and mix until fully incorporated, scraping down the sides of the bowl as needed.
Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract and continue mixing until the batter is completely smooth.
Pour the cheesecake mixture over the baked crust and spread it out evenly with a spatula.
Prepare the apple layer: In a medium bowl, combine the diced apples with sugar, cinnamon, and nutmeg. Toss until the apples are well coated in the mixture.
Evenly sprinkle the seasoned apples over the cheesecake layer.
Make the streusel topping: In the bowl of a stand mixer (or using a pastry cutter), combine the softened butter, brown sugar, flour, and oats. Mix until the mixture becomes crumbly and holds together when pressed.
Sprinkle the streusel evenly over the apple layer, covering as much of the surface as possible.
Return the pan to the oven and bake for 40-45 minutes, or until the center is set but still slightly wobbly when gently shaken.
Remove from the oven and let the bars cool to room temperature in the pan.
Once cooled, transfer the pan to the refrigerator and chill for at least 4 hours, or until fully set.
Lift the bars out using the parchment overhang, slice into squares, and drizzle with caramel sauce just before serving.