1In large bowl, beat sugars, peanut butter, shortening, butter and egg with electric mixer on medium speed, or mix with spoon. Stir in flour, baking soda, baking powder and salt. Cover; refrigerate about 3 hours or until firm.
2Heat oven to 375ºF. Shape dough into 1 1/4-inch balls. On ungreased cookie sheet, place balls about 3 inches apart. Flatten slightly in crisscross pattern with fork dipped in flour.
3Bake 9 to 10 minutes or until light brown. Cool 2 minutes; remove from cookie sheet to cooling rack. Cool completely, about 30 minutes. Spread chocolate frosting between bottoms of pairs of cookies.