1. Preheat your oven to 350°F (175°C) and line a 9×13-inch baking pan with parchment paper.
2. In a medium bowl, combine the flour and 1/2 cup sugar. Stir in the melted butter until the mixture resembles coarse crumbs.
3. Press the mixture evenly into the bottom of the prepared pan to form the crust. Bake for 15 minutes, until lightly golden. Set aside to cool slightly.
4. In a large bowl, beat the softened cream cheese and 1/2 cup sugar together until smooth. Add the eggs and vanilla extract, mixing well after each addition.
5. Pour the cream cheese mixture over the crust, spreading it evenly with a spatula.
6. In another bowl, combine the diced apples, 1/4 cup sugar, and cinnamon. Toss until the apples are well coated.
7. Scatter the apple mixture evenly over the cream cheese layer.
8. Drizzle the caramel sauce over the apples, reserving a little for serving.
9. Bake for 30-35 minutes, or until the cheesecake is set and the apples are tender.
10. Allow the bars to cool completely in the pan before slicing them into squares.

For a personal touch, I often add a sprinkle of nutmeg to the cinnamon-apple mixture, a little trick Mum taught me to enhance the cozy flavors.