Preheat the oven to 350 degrees F. and line a baking sheet with parchment paper and set it aside.

In the bowl of a stand mixer fitted with the paddle attachment, cream the butter, brown sugar, and granulated sugar together until light and fluffy. Add the egg and vanilla extract; mix until well combined.

Scrape down the sides of the bowl and then add the flour, cornstarch, baking soda, and salt. Mix until the dough is combined. Reserve a handful of chopped peanut butter cups and then fold in the remaining peanut butter cups and chocolate chips by hand or mix just until the chocolate is combined.

Using a scoop, roll the dough into balls, about 2 to 3 tablespoons each. Press a few reserved peanut butter cup pieces on top of the dough and place on the prepared baking sheet at least 2-inches apart.

Bake for 10 to 12 minutes, or until edges have just set and tops are just beginning to set. They will look slightly underbaked. Remove from the oven and let cool on the baking sheet for 10 minutes. Transfer to a metal rack to cool completely.