In an electric mixer, cream together butter and and sugars until smooth and fluffy. Scrape sides of the bowl.
Add in egg, mix until smooth and scrape the bowl. Repeat with peanut butter and vanilla.
Whisk baking soda, powder,salt and flour in a separate bowl and slowly add to the wet ingredients. Mix until no dry spots remain.
Scoop dough into 2-3 teaspoon balls and place on a lined baking sheet. Using the tines of a fork, gently press a criss-cross pattern into the top of each ball to slightly flatten. Sprinkle the tops with a bit of granulated sugar.
Bake at 350 degrees for 7-8 minutes. Do not overbake. Cookies are done when just lightly lightly browned on the bottom and just barely starting to get a little color around the edges.