Prepare your baking pan by preheating your oven to 350°F (175°C) and lining a 9×13-inch baking pan with parchment paper, leaving some overhang for easy removal later.
Make the crust by combining flour and brown sugar in a medium bowl, then cutting in the butter with a pastry blender or fork until the mixture resembles coarse crumbs. Press this mixture firmly into the bottom of your prepared pan.
Bake the crust for 15 minutes or until it’s lightly golden around the edges. Remove from the oven but keep the oven on.
Prepare the cheesecake layer while the crust bakes by beating the cream cheese with an electric mixer until smooth and creamy, about 2 minutes. Add sugar and beat until well combined, then add eggs one at a time, incorporating each fully before adding the next. Mix in vanilla extract.
Pour the cheesecake mixture over the warm crust, spreading it evenly with a spatula to create a smooth, level surface.
Create the apple layer by combining the chopped apples, sugar, cinnamon, and nutmeg in a bowl, tossing until all apple pieces are evenly coated. Distribute this mixture evenly over the cheesecake layer.
Make the streusel topping by mixing brown sugar, flour, and oats in a bowl. Add cubed butter and use your fingers or a fork to work it into the dry ingredients until crumbly. Sprinkle this mixture over the apple layer.
Bake the entire dessert for 30-35 minutes, until the streusel is golden brown and the cheesecake layer is set (it may still have a slight jiggle in the center).
Cool completely on a wire rack for at least 2 hours to allow the cheesecake to set properly. For best results, refrigerate for at least 2 additional hours or overnight.
Drizzle with caramel sauce just before cutting into bars. If the caramel sauce is too thick, warm it slightly before drizzling.
Cut into 16 squares using a sharp knife, wiping the blade clean between cuts for the neatest presentation.