Preheat your oven to 350 degrees.
In a mixing bowl, with the paddle attachment, cream together the softened butter, brown sugar, and granulated sugar for about 3 minutes or until the mixture is light and fluffy.
With the mixer on low speed, add the eggs and vanilla extract, mixing until well combined.
Slowly add the dry ingredients – all-purpose flour, baking powder, baking soda, cornstarch, and salt. Mix until the dough comes together and is well combined.
Gently fold in the roughly chopped Reese’s Peanut Butter Cups into the cookie dough.
Line a 9×9-inch baking pan with parchment paper, allowing some overhang on the sides for easy removal.
Press the cookie dough evenly into the prepared pan, creating a smooth and level surface.
Bake in the preheated oven for 30-35 minutes or until the top is golden brown and a toothpick inserted into the center comes out with a few moist crumbs. Be careful not to overbake.
Allow the cookie cake to cool in the pan for about 20 minutes. Then, using the parchment paper overhangs, carefully lift it out of the pan and transfer it to a wire rack to cool completely.
While the cookie cake is cooling, prepare the topping. In a microwave-safe dish, combine the Reese’s Peanut Butter Morsels and vegetable oil. Microwave in 30-second increments, stirring between each interval, until the morsels are completely melted and smooth.
Once the cookie cake has cooled completely, spread the melted peanut butter morsels over the top as a delicious topping.
Sprinkle the remaining chopped Reese’s Peanut Butter Cups over the melted morsels.
Allow the topping to set, either at room temperature or in the refrigerator, before slicing the cookie cake into wedges or squares.