Preheat oven to 350°. Place carrots in small saucepan and cover with water. Bring to boil, reduce heat and simmer until carrots are tender, about 10 minutes. Drain and mash with fork; cool. Combine sugar, shortening, ½ cup butter, eggs and mashed carrots in medium bowl. Beat until smooth. Mix flour, baking powder and salt in small bowl until well combined. Stir into creamed mixture until well blended. Stir in coconut. Drop by level tablespoonfuls about 2 inches apart on nonstick cookie sheets. Bake for 8 to 10 minutes or until golden brown around edges. Cool on wire rack.
Meanwhile, combine powdered sugar, orange juice, orange peel and butter in a small bowl. Beat until smooth. Spread cooled cookies with icing.
Makes 36 cookies.