1In large bowl, beat granulated sugar and shortening with electric mixer on medium speed, or mix with spoon. Stir in remaining cookie ingredients. Cover; refrigerate dough at least 3 hours or until firm.
2Heat oven to 375°F. Generously grease cookie sheet with shortening or cooking spray. On generously floured cloth-covered surface, roll half of dough at a time to 1/4-inch thickness. Cut with 3-inch round cookie cutter. Place about 1 1/2 inches apart on cookie sheets.
3Bake 10 to 12 minutes or until almost no indentation remains when touched lightly in center. Cool 2 minutes; remove from cookie sheets to cooling racks. Cool completely, about 30 minutes.
4In small bowl, mix glaze ingredients until smooth. Spread on cooled cookies.