Using the paddle attachment on the stand mixer, beat the butter, sugar, and brown sugar until light and fluffy.
Add the egg, vanilla, and peanut butter and mix to combine the ingredients.
Measure all the dry ingredients into the mixer bowl and slowly stir the ingredients until all the flour is mixed into the dough.
Remove the mixer bowl, cover with plastic wrap and refrigerate for 30 minutes.
Preheat oven to 375℉.
Remove dough from the refrigerator. Using your hands, roll dough into approximately 1½ tablespoon balls. Place 12 balls on a sheet pan and make a crisscross pattern on the top of each dough ball by lightly pressing the ball with the prongs of a fork.
Return the dough to the refrigerator between batches. In a standard sized home oven, 2 pans can be baked at a time.
Bake for 10 minutes.
After 10 minutes, remove the pan from the oven and allow the cookies to cool on the sheet pan for 5 minutes before transferring the cookies to the cooling rack to further cool down.
Continue steps 6-9 for the remaining cookies.
Cool for at least 10 minutes before serving. Store in an airtight container at room temperature for up to a week.