Preheat the oven to 350°F. Line a 9x13 baking pan with parchment paper. Set aside.
Crisp Topping
In a medium bowl, mix 1/2 cup all-purpose flour, 1/2 cup light brown sugar, 1/2 cup rolled oats, and 1/4 teaspoon salt. Add 6 tablespoons unsalted butter and using your fingers or a pastry cutter to mix the butter into the dry ingredients until crumbly and pieces of the butter are pea-sized. Spread the mixture evenly over the parchment-lined baking pan, then bake for 10-15 minutes or until the topping is golden brown. Use a spatula to break apart the topping and stir occasionally as it cools to make sure there are no large chunks. Cool to room temperature.
Caramelized Apples
Melt 4 tablespoons salted butter in a large skillet over medium heat. Stir in 3 peeled and chopped medium apples, and cook for 10 minutes or until the apples start to brown around the edges and are tender. Mix in the 1/2 cup packed light brown sugar, and remove from heat. Let the apples cool to room temperature.
Crust:
Grease a 9-inch springform pan with butter, and put it aside. Place the 9 graham crackers and 2 tablespoons brown sugar in a food processor and blend them until they are crushed into fine crumbs. Slowly pour in 8 tablespoons melted butter while running the processor at low speed until the crumbs are coated. Firmly press the crumbs into the bottom of the springform pan, then place it in the freezer for 15 minutes.
Cheesecake Filling
Use an electric mixer to blend 24 ounces cream cheese, 1/2 cup light brown sugar, 1 teaspoon cinnamon, and 1/2 cup plain Greek yogurt in a large mixing bowl until smooth. Fold in the thawed 8 ounces whipped topping.
Assembly
Spread the cheesecake filling over the frozen crust and smooth it out. Use a slotted spoon to spoon the apples over the cheesecake, then sprinkle the crisp topping on top. Cover the cheesecake with plastic wrap and chill it in the freezer for at least 4 hours but overnight is better.
Serve
When you are ready to serve, run a thin knife around the edge of the pan and carefully release the ring from the springform pan. Transfer the cheesecake to a large plate or cake stand. Serve chilled and top with caramel sauce, if desired.