Preheat oven to 350°F (175°C) and grease a 9x13 inch baking pan or line with parchment paper for easy removal.

In a medium bowl, combine flour and brown sugar. Cut in the softened butter using a pastry blender or fork until the mixture is crumbly. Press firmly into the bottom of the prepared pan and bake for 15 minutes.

In a large bowl, beat the cream cheese and granulated sugar with an electric mixer until smooth. Add eggs one at a time, beating well after each addition, then stir in the vanilla extract. Pour the mixture over the warm crust.

In a small bowl, toss the diced apples with sugar, cinnamon, and nutmeg. Spoon the apple mixture evenly over the cheesecake layer.

For the streusel, combine brown sugar, flour, and oats in a bowl. Cut in the chilled butter until the mixture resembles coarse crumbs. Sprinkle the streusel over the apple layer.

Bake for 40-45 minutes until the filling is set and the topping is golden brown. Let cool completely at room temperature, then refrigerate for at least 3 hours.

Once chilled, drizzle with caramel sauce and slice into bars before serving.