Preheat your oven to 350°F (175°C). Grease or line a 9x13-inch baking pan with parchment paper for easy lifting.
Make the crust by combining the flour and brown sugar in a bowl. Cut in the softened butter until the mixture is crumbly.
Press the crust mixture evenly into the bottom of the prepared pan.
Bake for 15 minutes, or until lightly golden. Remove from the oven and let it cool slightly.
While the crust bakes, prepare the cheesecake filling. Beat the cream cheese and sugar until smooth and creamy.
Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract.
Pour the cheesecake filling over the warm crust and spread evenly.
In a separate bowl, toss the chopped apples with sugar, cinnamon, and nutmeg.
Spoon the apple mixture evenly over the cheesecake layer.
Make the streusel topping by combining brown sugar, flour, and oats. Cut in the softened butter until coarse crumbs form.
Sprinkle the streusel evenly over the apples.
Bake the Caramel Apple Cheesecake Bars for 30 to 35 minutes, or until the center is set and the topping is golden.
Cool completely in the pan, then chill for at least 3 hours until firm.
Drizzle with caramel topping before slicing into bars and serving.