Preheat oven to 350 degrees. In a small mixing bowl, whisk together flour, baking soda and salt, set aside. In the mixing bowl of an electric mixer, mix together butter, peanut butter, granulated sugar and brown sugar until light and fluffy.
Stir in egg and vanilla. Slowly add dry ingredients. Scoop out 1 even tablespoon of dough at a time and roll into a small ball. Set dough balls on greased cookie sheet and bake 7 - 9 minutes.