Preheat oven to 350F. Line an 8x8 baking pan with parchment paper or aluminum foil greased with non-stick cooking spray. Set aside.
In a large bowl, combine flour and brown sugar. Cut in butter with a pastry blender or hands. Combine until it resembles a course mixture. Press into the bottom of prepared pan.
Bake for 10-12 minutes, or until crust is lightly browned. Set aside.
While crust is baking, prepare the apples and cheesecake batter. In a small bowl, combine the apples, cinnamon, white sugar, and nutmeg. Set aside.
In a large bowl, beat the cream cheese until soft and creamy with an electric hand mixer or stand mixer with fitted paddle attachment. Add in egg, sugar, vanilla, and apple pie spice, beating well to thoroughly combine.
Pour batter onto prepared crust and spread evenly. Sprinkle seasoned apples over top.
In a small bowl, combine the brown sugar, flour, old-fashioned oats, and butter until crumbly. Sprinkle evenly over cheesecake batter.
Bake for 40-45 minutes, or until cheesecake filling is set. Remove from oven and let cool for at least one hour.
Drizzle with caramel sauce and cut into bars.