Preheat oven to 350°F. Line a 9×9-inch baking dish with parchment paper, including up the sides for easy removal.
In a medium bowl, combine graham cracker crumbs, melted butter, and granulated sugar. Stir until the mixture resembles wet sand.
Press the mixture evenly and firmly into the bottom of the prepared baking dish.
In a large bowl, using a hand mixer on medium speed, beat cream cheese until smooth.
Add eggs, granulated sugar, vanilla extract, and salt. Beat again until creamy and well blended.
Spread the filling evenly over the crust.
In a small bowl, toss diced apples with granulated sugar, cinnamon, and nutmeg until evenly coated.
Scatter the spiced apples evenly over the cream cheese filling.
In a medium bowl, whisk together flour, brown sugar, kosher salt, and cinnamon. Stir in melted butter until the mixture forms a crumbly dough. (Do not overmix.)
Sprinkle the crumble evenly over the apples.
Bake for 35-40 minutes, or until the filling is set and the crumble topping is golden brown.
Transfer the baking dish to a wire rack and let cool completely for about 1 hour, then refrigerate for at least 1 hour before slicing.
Just before serving, drizzle slightly warmed caramel sauce over the top of the chilled bars.