In medium bowl combine flour, baking soda, baking powder and salt.
In mixer bowl cream butter or margarine, peanut butter, brown sugar, and 1 cup granulated sugar until light and fluffy. Beat in eggs and vanilla. Gradually beat in dry ingredients until just combined.
Shape tablespoonfuls of dough into 1-inch balls and roll in remaining 1/3 cup granulated sugar. Place 3-inches apart on 2 ungreased cookie sheets. With sugar-coated tines of a fork, press and flatten each ball, making a criss-cross pattern.
Bake 8-10 minutes, until golden.
Cool on cookie sheets 5 minutes; transfer to racks to cook completely.