Preheat the oven to 350°F. Line a 9x13 baking pan with parchment paper. Set aside.

In a medium bowl, mix the flour, brown sugar, oats, and salt. Add the 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.

Melt the butter in a large skillet over medium heat. Stir in the apples, and cook for 10 minutes or until the apples start to brown around the edges and are tender. Mix in the brown sugar, and remove from heat. Let the apples cool to room temperature.

Grease a 9-inch springform pan with butter, and put it aside. Place the graham crackers and brown sugar in a food processor and blend them until they are crushed into fine crumbs. Slowly pour in the 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.

Use an electric mixer to blend the cream cheese, brown sugar, cinnamon, and yogurt in a large mixing bowl until smooth. Fold in the thawed whipped topping.

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.

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.