Adjust rack to center of oven and heat to 350° F. In a large bowl, combine the flour, baking powder, baking soda, and salt; set aside. In a bowl, with an electric mixer on medium, beat the butter until light and fluffy. Add 1/2 cup of the granulated sugar, the brown sugar, and vanilla and beat until incorporated. Add the egg and combine, then add the peanut butter. Reduce speed to low, add the flour mixture, and beat until incorporated. Stir in the peanuts. Form the dough into 1 1/2-inch balls. Roll in the remaining sugar and place on a baking sheet, 2 inches apart. Using the back of a fork, gently press the cookies to form a crisscross pattern. Bake 12 to 16 minutes or until just golden. Cool on racks.