Using a hand mixer on low speed, cream shortening and sugars together in a large bowl.
Add egg and vanilla extract and beat on low until just combined.
Add flour, cornstarch, baking soda and salt and mix until flour is just incorporated.
Fold in Reese's pieces and chocolate chips.
Cover with plastic wrap and chill for 2 hours or overnight.
Remove dough from fridge and let sit at room temperature for 5 minutes.
Meanwhile, preheat oven to 350°F and line cookie sheets with parchment paper or silicone mat.
Roll dough into 18 even balls and place on prepared pans.
Bake 12-16 minutes. Cookies will still look a little wet in the middle.
Cool on racks. Then store in airtight containers.