In a large mixing bowl beat 1/2 cup butter and 1/2 cup peanut butter with an electric mixer on medium to high speed for 30 seconds. Add 1/2 cup granulated sugar, 1/2 cup brown sugar, 1/2 teaspoon baking soda, and 1/2 teaspoon baking powder. Beat until combined, scraping sides of bowl occasionally.
Beat in one egg and 1/2 teaspoon vanilla until combined.
Beat in as much of the 1 1/4 cups of 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 chiled 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. Cool on a wire rack.
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Once you know how to make peanut butter cookies, try these delicious takes on our classic peanut butter cookie recipe. We've got tasty combinations like peanut butter and chocolate, peanut butter and jelly, and peanut butter and banana.