Chef John's Peanut Butter Cookies

Beat butter, white sugar, brown sugar, peanut butter, salt, baking powder, and baking soda in a stand mixer until smooth.
Scrape down the sides of the bowl and beater with a spatula. Add egg and mix for about 1 minute.
Slowly mix in flour with the mixer on low. Scrape down the sides of the bowl and beater. Mix on medium until combined, about 30 seconds.
Form dough into a ball, cover with plastic and refrigerate for 2-3 hours.
Preheat the oven to 375 degrees F (190 degrees C).
Portion out cookie dough in equal-sized balls on a baking sheet covered with a silicone baking mat. Use damp hands to roll dough into smooth balls. Stamp each ball with a fork in a criss-cross pattern.
Bake in the preheated oven for 10 minutes until golden.
Leave on the baking sheet for 5 minutes before transferring to a cooling rack.