Preheat oven to 350°F and line a 9x9-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.
Pour crust mixture into the prepared baking pan and gently press the mixture evenly into the bottom of the pan. Bake for 10 minutes.
While the crust is baking, beat the cheesecake ingredients together in a medium bowl until smooth and creamy and set aside.
Add finely chopped pears to a medium saucepan and add in the lemon juice, stirring to coat, and cook over medium-high heat for 5 to 7 minutes until pears 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 pears and cook for another 2 minutes, stirring constantly, once 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 pear filling. Top the pear filling with the crumble topping.
Bake cheesecake bars for 60 to 70 minutes, remove from 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.