In a large bowl or stand mixer, cream together peanut butter, softened butter, granulated sugar, and brown sugar on medium speed for 3 minutes until light and fluffy.
Add eggs one at a time, mixing well after each addition. Stir in vanilla extract until combined.
In a separate bowl, whisk together flour, baking soda, salt, and cornstarch.
Gradually add dry ingredients to wet mixture, mixing on low speed until just combined. Dough will be thick and slightly sticky.
Cover bowl and refrigerate dough for at least 1 hour to firm up the butter.
Preheat oven to 350°F (175°C). Line two baking sheets with parchment paper.
Scoop dough into 1½-tablespoon portions and roll into smooth balls. Roll each ball in granulated sugar.
Place cookies 2 inches apart on prepared baking sheets. Use a fork to press criss-cross pattern on top of each cookie.
Bake for 10-12 minutes until edges are lightly golden but centers still look slightly underdone.
Cool cookies on baking sheet for 10 minutes before transferring to wire rack to cool completely.