In a large bowl, cream together butter and sugars. Beat in egg. Add vanilla and peanut butter and beat well. Add in dry ingredients and beat on low speed until combined.
Drop by rounded spoonfuls onto parchment lined baking sheet.
Using a fork, mark grids on the top of each cookie, dipping the fork in water after each cookie.
Bake for 11-12 minutes, until just beginning to brown on the edges.
Cool on wire rack.
Note: I use natural, salted peanut butter. You get a more buttery cookie by using the natural peanut butter, since it doesn’t have all that extra sugar. The cookie will also be more brittle/crumbly if you use processed peanut butter, so I would recommend adding an extra tablespoon of butter.