Preheat the oven to 350°F (175°C). Grease or line a 9×13-inch baking pan with parchment paper or heavy-duty aluminum foil.
In a medium bowl, combine the flour and brown sugar for the crust. Cut in the softened butter until the mixture becomes crumbly. Press evenly into the prepared pan.
Bake the crust for 15 minutes, or until lightly golden.
In a large bowl, beat the softened cream cheese with the sugar until smooth. Add the eggs one at a time, then stir in the vanilla extract.
Pour the cheesecake filling evenly over the warm crust.
In a small bowl, combine the chopped apples with sugar, cinnamon, and nutmeg. Spread evenly over the cheesecake layer.
Prepare the streusel by mixing brown sugar, flour, oats, and softened butter until crumbly.
Sprinkle the streusel evenly over the apples.
Bake the Caramel Apple Cheesecake Bars for 40–45 minutes, or until the cheesecake is set and the topping is lightly golden.
Allow the bars to cool completely at room temperature before refrigerating for at least 3 hours.
Drizzle generously with caramel topping before slicing and serving.