Prepare the oven and baking sheets. Preheat the oven to 350°F (175°C). Line baking sheets with parchment paper.
Combine the dry ingredients. Sift the flour, baking powder, and cornstarch into a bowl. Set aside.
Cream the butter and sugars. Beat the softened butter, brown sugar, and granulated sugar with a mixer until creamy and well combined. Scrape down the sides of the bowl.
Add the peanut butter. Beat in the peanut butter until evenly incorporated.
Mix in the egg and vanilla. Add the egg and vanilla extract. Beat until combined, scraping the sides and bottom of the bowl as needed.
Add the dry ingredients. Gradually mix in the flour mixture on low speed just until no dry flour remains. Avoid overmixing.
Shape the cookies. Divide the dough into 32 portions and roll into small balls. Arrange on the prepared baking sheets about 2 inches (5 cm) apart.
Make the fork marks. Gently flatten each ball with a fork, then press again in the opposite direction to create a crisscross pattern.
Bake. Bake each tray for about 10 minutes, until the edges are set and the tops no longer look wet. The centers may still feel soft.
Cool. Allow the cookies to cool on the baking sheet before moving them. They will firm up as they cool.
