Preheat oven to 350 degrees. Spray a 9x13 baking pan with cooking spray. Set aside
In a small bowl, combine flour, brown sugar, and cold cubed butter. Use a pastry cutter or hands to mix until crumbly. Press into the baking pan. Bake 16-20 minutes or until lightly browned.
In a separate bowl combine all the cheesecake ingredients (cream cheese, sugar, vanilla, and eggs) and beat together until smooth and combined.
In a small bowl, combine the peeled and chopped apples with the sugar, cinnamon. Mix together until the apples are coated.
Pour the cheesecake mixture over the cooked crust and spread out evenly. Sprinkle the apples over the cheesecake.
Prepare the streusel topping by combining all the ingredients . Use your hands or a pastry cutter to combine until crumbly like wet sand. Spread it evenly over the apples.
Cook for 25-30 minutes. The edges should be done and slightly pulled away from the edges of the pan. The middle should be soft set but not runny
Remove from oven and put on a cooling rack. Drizzle the caramel sauce over the bars and let cool at room temperature for 1 hour. Cover the dish and put in the refrigerator for 3 hours. Cut into bars and serve. Store leftovers in the fridge. I use ice cream topping and put extra on when served.