Combine peanut butter, butter, granulated sugar, brown sugar, salt, baking soda, baking powder, and vanilla extract in the bowl of a stand mixer fitted with a paddle attachment (or a large bowl if using a hand mixer). Mix ingredients on low speed to moisten, then increase the speed to medium (#4 if using a Kitchen Aid stand mixer) and beat until soft and light, approximately 3 minutes. Periodically scrape down the sides of the bowl to ensure all ingredients are incorporated.