Preheat the oven to 350°F. Line baking sheets with parchment paper or leave them ungreased.
In a medium bowl, whisk together 2 1/2 cups all-purpose flour, 1 teaspoon baking powder, 1 teaspoon baking soda, 1 teaspoon cornstarch, and 1 teaspoon salt. Set aside.
In a large mixing bowl, beat 1 cup softened butter, 1 1/4 cups sugar, and 1 cup brown sugar until light and fluffy, about 2–3 minutes.
Add 1 cup peanut butter, 2 large eggs, and 1 teaspoon vanilla extract. Beat until well combined.
Gradually add the dry ingredients to the peanut butter mixture, mixing on low speed just until the dough comes together. Do not overmix.
Scoop the dough into 36 portions and roll each portion into a ball.
Roll each dough ball in the remaining sugar, then place them on the prepared baking sheets, leaving about 2 inches between each cookie.
Using a fork, gently flatten each dough ball and make a crisscross pattern on top.
Bake for 10–12 minutes, or until the edges are lightly golden and the centers are set.
Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.
Serve and enjoy.