In a large mixing bowl beat butter and peanut butter with an electric mixer on medium to high speed for 30 seconds. Add the granulated sugar, brown sugar, baking soda, and baking powder. Beat until combined, scraping sides of bowl occasionally. Beat in the egg and vanilla until combined. Beat in as much of the flour as you can with the mixer. Stir in any remaining flour. If necessary, cover and chill dough about 1 hour or until easy to handle.

Preheat oven to 375 degrees F. Shape dough into 1-inch balls. Roll balls in additional granulated sugar to coat. Place balls 2 inches apart on an ungreased cookie sheet. Using the tines of a fork, flatten balls by making crisscross marks on top. Bake for 7 to 9 minutes or until bottoms are light brown. Transfer to a wire rack and let cool. Makes about 36 cookies.

Layer cookies between waxed paper in an airtight container; cover. Store at room temperature for up to 3 days or freeze for up to 3 months.