Preheat your oven to 350°F and prepare your baking sheet with either parchment paper or a silicone baking mat.
In a large bowl, whisk together the flour, baking powder, baking soda, cornstarch, and salt. Set aside.
In a mixer fitted with a paddle attachment (or using a hand mixer), cream the butter, granulated sugar, and brown sugar together on medium speed until the mixture is fluffy and pale, about 3 minutes.
Add the peanut butter and continue mixing until fully incorporated and smooth.
Mix in the vanilla extract and eggs one at a time, beating briefly between each addition. Scrape down the bowl as needed.
Reduce the mixer speed to low and slowly add in the dry ingredients. Mix just until the dough is smooth—do not overmix.
Scoop the dough using a small batter scoop and place onto your baking sheet. Press a fork into each dough ball to flatten slightly and create the classic crisscross pattern. Leave about 2 inches of space between cookies.
Bake for 10–12 minutes, or until the edges are lightly golden. Allow cookies to cool on the sheet for 10 minutes before transferring to a wire rack to cool completely.