In a large bowl, cream butter, peanut butter and sugars. Add eggs, one at a time, beating well after each addition. Beat in vanilla. Combine the flour, baking powder and baking soda; gradually add to creamed mixture. Refrigerate for 1 hour.
Roll dough into 1-in. balls; roll in sugar. Shape into logs. Place 2 in. apart on ungreased baking sheets. Flatten with a fork. Pinch center to form peanut shape. Bake at 375° for 7-10 minutes or until golden brown. Cool for 2 minutes before removing to wire racks.