Preheat the oven to 350°F (175°C).
In a medium bowl, combine flour and brown sugar for the crust. Cut in the softened butter using a pastry blender, forks, or food processor until the mixture becomes crumbly.
Press the crust mixture evenly into a greased or parchment-lined 9x13-inch baking pan. Bake for 15 minutes until lightly golden.
In a large bowl, beat the cream cheese and sugar using an electric mixer until smooth.
Add the eggs one at a time, mixing after each addition. Stir in the vanilla extract.
Pour the cheesecake mixture over the warm crust.
In a small bowl, mix the chopped apples with sugar, cinnamon, and nutmeg.
Evenly distribute the apple mixture over the cheesecake layer.
To prepare the streusel topping, combine brown sugar, flour, oats, and softened butter in a bowl. Use your hands or a pastry cutter to mix until crumbly.
Sprinkle the streusel evenly over the apple layer.
Bake for 40–45 minutes, or until the filling is set and the topping is golden.
Allow the bars to cool to room temperature, then refrigerate.
Before serving, drizzle caramel topping over the bars. These Caramel Apple Cheesecake Bars taste best when chilled.