1Stir together sugars, peanut butter, shortening, butter and egg in large bowl. Stir in flour, baking soda, baking powder and salt. Cover and refrigerate about 2 hours or until firm.
2Heat oven to 375ºF. Shape dough into 1 1/4-inch balls. Place about 3 inches apart on ungreased cookie sheet. Flatten in crisscross pattern with fork dipped in granulated sugar.
3Bake 9 to 10 minutes or until light brown. Cool 5 minutes; remove from cookie sheet to wire rack. Cool completely.
4For each ice-cream sandwich, press 1 rounded tablespoon ice cream between 2 cookies. Roll the edges of the sandwiches in candies. Wrap each sandwich in plastic wrap. Store sandwiches airtight in freezer.