Preheat oven to 350°F (175°C). Grease and flour a 13×9-inch baking dish.
In a bowl, mix graham cracker crumbs, ¼ cup sugar, and melted butter for the crust.
Press the crust evenly into the prepared dish. Bake for 10 minutes, then cool.
In another bowl, combine cream cheese (room temperature), ½ cup sugar, eggs, and vanilla extract until smooth. Spread over cooled crust.
In a skillet, sauté apple slices with butter, 2 tbsp flour, cinnamon, nutmeg, and brown sugar. Cook 5-7 minutes until tender. Spread apples over cheesecake layer.
Bake 25 minutes or until center is set. Cool completely.
For caramel: Combine sugar, water, salt, and corn syrup in a saucepan. Cook over medium heat to 350°F (175°C), stirring until smooth. Remove from heat, stir in heavy cream until thickened. Drizzle over cooled bars.
Chill at least 1 hour before cutting into 16 bars.