In a large bowl, add butter and both sugars, Mix on medium-high with either hand mixer or stand mixer until the mixture is light and fluffy.
Add the ½ cup of peanut butter and continue to mix until incorporated.
Add in the egg and vanilla and mix again until the egg is combined completely into the mixture.
In a separate bowl, sift the flour, baking soda, baking powder, and salt.
Dump the dry ingredients into the wet and mix on low until most of the flour is combined. You can then bump the speed to medium and mix until the dry ingredients are mixed into the wet and a round ball of dough has formed.
Using two spoons or a cookie scoop, scoop the dough into balls on a baking sheet.
Use a fork and put a T-shape into the cookie. This will flatten the cookie out and give it the well known design for peanut butter cookies.
Bake for 8 minutes. Let them cool for a minute or two before you transfer the cookies onto a cooling rack or they may break.