Place your Reese’s Cups in the freezer so that they will harden and be easy to stuff in the cookie dough.
In the bowl of a stand mixer (or in large bowl using electrical mixer), cream together butter, peanut butter, and sugars until light and fluffy. Scrape sides of bowl.
Add eggs and vanilla extract. Beat until well-combined (again, pause to scrape down the sides of bowl, as needed).
In a separate bowl, whisk together flour, cornstarch, baking powder, baking soda, and salt.
Gradually add flour mixture to batter while stirring on low speed until completely combined.
Stir in chocolate chips.
Place dough in refrigerator to chill 15-30 minutes (if dough is too sticky at 15 minutes, allow it to chill longer, it should be soft and pliable, but not messy).
Remove chilled dough from fridge and Reese’s cups from freezer. Remove peanut butter cups from their wrappers.
Scoop dough by heaping 1 ½ Tbs-sized spoonful and press peanut butter cup sideways into the center. Scoop more dough, as needed, and form around peanut butter cup until it is completely concealed. Roll into round ball and place on a wax-paper lined plate or tray. Return cookie dough balls to refrigerator for 15 minutes.
Preheat oven to 375F (190C) and line cookie sheets with parchment paper.
Place cookie dough balls at least 2″ apart on cookie sheet and bake on 375 (190C) for 14 minutes, or until edges are just beginning to turn golden brown.
Allow cookies to cool completely on cookie sheet (they will be very fragile when hot) before serving. Enjoy!