Preheat the oven to 350 degrees. Line a baking sheet or two with parchment paper or a silicone liner.
Add the butter and peanut butter to a large bowl and mix them together until combined.
Add in the sugars and cream the mixture for about 2 minutes, or until the mixture is light and fluffy.
Add in the egg, and vanilla extract and stir them until just combined.
Add in the dry ingredients, and stir them into the mixture to make a nice soft cookie dough.
Cover the dough and place it in the fridge for 1 hour to chill.
Scoop 1.5 tablespoon sized balls of cookie dough, and roll them into balls. Roll them into granulated sugar if desired.
Place them onto the prepared cookie sheet a couple inches apart.
Slightly flatten the balls with a fork, making a criss cross pattern.
Bake the cookies in the oven for 8-9 minutes, or until the edges of the cookie are lightly golden and the tops are almost set.
Remove the cookies from the oven and let the cookies the cookies sit on the cookie sheet for 5 to 10 minutes. Then transfer them to a cooling rack.