In a large mixing bowl, cream the butter, peanut butter and sugars. Add egg; beat well. Beat in vanilla. Combine the flour, baking powder and baking soda; gradually add to creamed mixture.
Insert a lollipop stick into one side of each candy bar until stick is nearly at the opposite side. Press one heaping tablespoon of dough around each candy bar until completely covered. Press dough tightly around the end of the candy bar and the stick.
Place three inches apart on lightly greased baking sheets. Bake at 350 degrees for 14-16 minutes or until cookies are set. Cool for 1-2 minutes before removing from pans to wire racks to cool completely.