Place a sheet of parchment paper on a large baking sheet. Set aside.
Add butter and sugars into a bowl of a stand mixer fitted with a paddle attachment and beat together on medium until fluffy, about 3 minutes. Add egg and vanilla and beat until combined. Add peanut butter and mix until smooth. In a separate bowl, mix flour, baking soda, baking powder, and salt until combined. Add all of the dry ingredients to the wet ingredients and mix on low just until combined.
Scoop dough into 1.5 tablespoons onto the prepared baking sheet. Dough balls can be touching. Cover with plastic wrap and chill for 2 hours in the fridge.
Once dough is ready, preheat oven to 350 degrees. Prepare another baking sheet by adding parchment paper or a silicone mat. Remove dough from fridge.
Roll dough into smooth, round balls. Place on baking sheet, 2 inches apart. Using a fork, push down the back of the tongs into the dough into a cross pattern. Bake for 12 minutes, or until the edges crispy very slightly.
Remove from oven and let cook for 10 minutes and then transfer to cooling rack to cool completely. I placed mine in the fridge to help the process along.