Preheat the oven to 350°F and line a 9″x 9-inch baking pan with parchment paper and set aside.
Combine shortbread cookie crumbs and sugar in a medium bowl and make a small well. Pour the melted butter in the well and mix until evenly combined.
Transfer the crust mixture to the prepared baking pan and gently press the mixture evenly into the bottom of the pan. Bake for 8 minutes.
While the crust is baking, beat together the cheesecake ingredients in a medium bowl until smooth and creamy and set aside.
Add the diced apples and lemon juice to a medium saucepan and cook over medium-high heat for 5 to 7 minutes until apples are tender and juice has started to form.
In a separate bowl, combine the brown sugar, cinnamon, nutmeg, and cornstarch. Then stir it into the apple mixture and cook for another 2 minutes, stirring constantly. Once the mixture has thickened and resembles pie filling, remove from heat.
To make the oatmeal crumble, combine all ingredients in a large bowl and use a pastry cutter or your fingers to mix the ingredients together, squishing the cubes of butter and creating a coarse crumble.
Now it’s time to start assembling the cheesecake bars. Pour the cheesecake mixture over the baked crust and spread out evenly. Top the cheesecake mixture with the apple filling. Top the apples with the crumble topping.
Bake cheesecake bars for 50 to 70 minutes, until the top of the crumble is a light golden brown. Remove from the oven and let cool in pan on a wire rack for 30 minutes. Transfer to the refrigerator to cool for at least 4 hours, preferably overnight.
Slice into square bars and drizzle with caramel just before serving. Top with a dollop of whipped cream if desired.