In the bowl of a mixer fitted with the paddle attachment, cream together the softened butter, brown sugar, and granulated sugar for about 3 minutes until light and fluffy.
Add the eggs and vanilla extract to the mixer on low speed, mixing until well combined.
Slowly add in the all-purpose flour, baking powder, baking soda, cornstarch, and salt. Mix until the dry ingredients are fully incorporated.
Stir in the chopped Reese’s Peanut Butter Cups until evenly distributed in the dough.
On a large sheet pan lined with parchment paper, scoop out 3 tablespoons of cookie dough for each cookie. Chill the cookie dough in the fridge for 30 minutes. (This recipe makes about 10 cookies. You can place them on one pan for chilling but separate them into two pans when ready to bake.)
Preheat the oven to 350 degrees Fahrenheit (175 degrees Celsius).
Place 6 cookies per pan on a lined baking sheet. Press down the cookie dough to form flat disks using the bottom of a cup.
Bake the cookies for 12-13 minutes until they are lightly golden. Let the cookies cool for 2-3 minutes, then use the bottom of the cup to gently flatten the tops. Transfer the cookies to a wire rack to cool completely.
In a microwave-safe dish, melt the Reese’s Peanut Butter Morsels and vegetable oil in 30-second increments, stirring in between, until everything is melted and smooth.
Top the cooled cookies with some of the melted morsels and sprinkle with chopped Reese’s Peanut Butter Cups.
Allow the topping to set before serving. These delicious Reese’s Peanut Butter Cup cookies are now ready to enjoy!