Preheat oven to 350 degrees F. Spray an 8x8-inch square baking dish with cooking spray. Cut a piece of parchment to fit the width of the pan and line the pan with the parchment, letting it overhang on two opposite sides. Spray the parchment with cooking spray.

In a food processor, process 1 ½ cups of the oats until finely ground. Add in the brown sugar, cinnamon, and salt and process until combined. Add in the butter pieces and pulse 8 times, until the largest pieces of butter are the size of small peas. Add in the remaining 1 cup oats and process in 5 quick pulses.

Press half of the crumble mixture into the bottom of the prepared baking dish. Bake for 18 minutes and then place on a wire rack to cool slightly. The crust should be light golden brown, and will be soft and not set when you remove it from the oven. It will set up as it cools. Maintain oven temperature at 350 degrees.

While the crust bakes and cools, make the caramel apples. Combine all ingredients in a medium saucepan. Cook over low heat, stirring often, for 15 minutes, until apples are soft. Remove from heat.

Wipe out any crumble crumbs off of the blade and bowl of the food processor. Combine all cheesecake ingredients in the bowl of the food processor. Process until smooth, scraping down the sides of the bowl as needed.

Pour the cheesecake on top of the crust in the baking dish. Scoop the apples on top of the cheesecake in an even layer. Crumble the remaining crust/crumble mixture over the top of the apples. Bake at 350 degrees until the crumble is golden and cheesecake is set, 40-45 minutes. Cool completely and then refrigerate for at least 4 hours before slicing and serving. (The bars taste even better on the second and third day, if you have time to chill them overnight.)