In a mixing bowl, cream together ½ cup of softened butter and ⅓ cup of granulated sugar until light and fluffy, about 3-4 minutes. Gradually add in 1 cup of all-purpose flour, mixing until a soft dough forms. Press the dough evenly into the bottom of a greased 9x9 inch baking pan. Bake in a preheated oven at 350°F (175°C) for 15-20 minutes or until the crust is lightly golden.

While the crust bakes, prepare the filling. In a large bowl, beat 8 oz of softened cream cheese with ⅓ cup of granulated sugar until smooth, about 2-3 minutes. Add in 2 large eggs, one at a time, mixing until fully incorporated.

In a small saucepan, combine 1 cup of blueberries and 1 tablespoon of cornstarch over medium heat. Stir occasionally while bringing them to a simmer, cooking for about 3-5 minutes until the blueberries burst and the mixture thickens and becomes glossy.

Once the crust is ready and cooled slightly, pour the cream cheese filling evenly over the crust. Dollop the blueberry mixture on top and swirl it through the filling with a knife.

Return the pan to the oven and bake for an additional 25-30 minutes, or until the filling is just set but still slightly jiggles in the center.

After baking, remove the bars from the oven and let them cool at room temperature for about 30 minutes. Transfer the pan to the refrigerator and allow it to chill for at least 3-4 hours, or overnight for best results.