In a large bowl, whisk together flour, baking soda, baking powder, and salt.
Using a stand or hand mixer, beat butter and sugars on medium speed until very fluffy, 2 minutes. Beat in eggs one at a time, mixing well after each addition. Add peanut butter and continue mixing until mixture is completely smooth and fluffy, 2 to 3 minutes more.
Add flour mixture in batches and continue mixing, scraping sides of bowl as you go. Refrigerate batter 1 hour.
When ready to bake, preheat oven to 350° and line two baking sheets with parchment. Drop tablespoons of dough on prepared baking sheets, about 2” apart.
Using a fork, score cookies with a cross-hatch pattern.
Bake until golden, 15 to 18 minutes. Transfer to wire rack to let cool before serving.