In a medium-sized bowl, vigorously whisk together the flour, baking soda, baking powder, and salt.
In a stand mixer fitted with the paddle attachment (or with an electric mixer), cream the butter on medium-high speed until pale and smooth, approximately 2 minutes. Add both sugars and cream for an additional 2-3 minutes. Add the peanut butter, followed by the egg, until the ingredients are smooth. Add the dry ingredients, mixing on low speed or stirring with a spatula until evenly combined.
Cover the bowl with plastic film, pressing against the dough to prevent a crust. Chill for at least 3 hours.
Preheat the oven to 300 degrees F. Line a baking sheet with parchment paper.
Use a 1-tablespoon scoop to shape the dough into balls, placing them 3 inches apart on the prepared sheet. (Note: these cookies spread out a lot; you’ll likely be baking in batches).
Briefly roll the balls to smooth them out, then use a fork to flatten in a crisscross pattern. You can dip the fork in a bowl of sugar to help prevent sticking.
Bake the cookies for 15 minutes, until light brown. Allow to cool for a few minutes on the sheet, then transfer to a wire rack to finish cooling.
Store in an airtight container at room temperature for several days. After that, I recommend freezing them to preserve the texture and flavor.
Notes
If you don’t eat peanut products, these cookies are amazing with cashew butter. Cashews have a more subtle flavor that work so well in these chewy cookies. Recipe barely adapted from Simply Recipes.