Preheat oven to 400°F and line two large baking sheets with parchment paper.
In a stand mixer with paddle attachment, beat butter, brown sugar, and peanut butter on medium-high speed until light and creamy, about 3-5 minutes.
Add vanilla extract and mix to combine.
Add eggs one at a time, mixing well after each addition.
In a separate bowl, whisk together flour, baking soda, cornstarch, and salt.
Gradually add dry ingredients to wet ingredients and mix on low speed until just combined.
Fold in peanut butter chips and Reese's Pieces by hand.
Chill the dough in the refrigerator for 15 minutes.
Scoop dough with a 1/4 cup measure onto prepared baking sheets, spacing about 3 inches apart.
Flatten each dough ball slightly with hands or the bottom of a glass.
Bake 8-10 minutes until edges are set and tops are golden brown; centers will remain gooey.
Allow cookies to cool on baking sheets for at least 30 minutes before serving.