Preheat oven to 350 degrees. Spray a 9x13 baking pan with cooking spray. You can also use parchment paper and spray the parchment paper. Set aside.
Make the crust: 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 15-18 minutes or until lightly browned.
While the crust is baking prepare the cheesecake. Combine all the cheesecake ingredients (cream cheese, sugar, vanilla, and eggs) into a bowl, or bowl of a stand mixer, and beat together until smooth and combined.
In a small bowl, combine the peeled and chopped apples with the sugar, cinnamon, and nutmeg. 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 (NOT the caramel sauce). Use your hands or a pastry cutter to combine until crumbly like wet sand. Sprinkle 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 totally liquid/jiggly.
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.
PLAN AHEAD : These bars cool for 1 hour + need to be refrigerated for 3 hours before serving. You can also make them the day before and leave them in the fridge until serving.
Make sure the cream cheese is very soft to avoid lumps in the cheesecake. I place the unwrapped cream cheese bars on a microwave-safe plate and cook them for about 30-40 seconds or until they are very soft.