Preheat your oven to 350°F (175°C). Grease an 8x8-inch baking dish or line it with parchment paper for easy removal.
In a medium bowl, combine the blueberries, lemon juice, granulated sugar, and cornstarch. Gently toss to coat the blueberries and set aside.
In another bowl, mix together the flour, rolled oats, brown sugar, cinnamon, and salt. Pour in the melted butter and stir until the mixture is crumbly.
Press half of the oat mixture into the bottom of the prepared baking dish to form a crust. Bake for 10 minutes, then remove from the oven.
While the crust is baking, prepare the cheesecake layer. In a mixing bowl, beat the softened cream cheese, powdered sugar, vanilla extract, and egg until smooth and creamy.
Spread the cheesecake mixture evenly over the baked crust. Spoon the blueberry mixture over the cheesecake layer, distributing it evenly. Finally, sprinkle the remaining oat mixture on top.
Return the dish to the oven and bake for an additional 25-30 minutes, or until the topping is golden brown and the cheesecake is set. Allow to cool completely in the pan before slicing into bars.
Serve chilled or at room temperature. For best results, refrigerate for at least 2 hours before serving.