In a medium bowl, whisk flour, baking soda, baking powder, and salt.
In a large bowl, using a handheld mixer on medium speed, beat butter, brown sugar, and granulated sugar until very fluffy, about 2 minutes.
Add eggs one at a time, beating to blend after each addition.
Add peanut butter and continue to beat until smooth and fluffy, 2 to 3 minutes more.
Add dry ingredients in 3 batches and beat on medium-low speed, scraping down sides of bowl as needed, until no dry streaks remain.
Refrigerate batter until very cold, about 1 hour.
Preheat oven to 350° and line 2 baking sheets with parchment.
Drop tablespoons of dough on prepared sheets, spacing about 2" apart.
Using a fork, score top of dough with a crosshatch pattern.
Bake cookies until golden, 15 to 18 minutes.
Transfer to wire rack and let cool.
