Heat oven to 375°F. Spray cookie sheets with nonstick cooking spray.
In large bowl, combine sugar, shortening, molasses, water and egg; beat well. Lightly spoon flour into measuring cup; level off. Add all remaining cookie ingredients; stir just until blended. Let stand 5 minutes. Drop by rounded teaspoonfuls 2 inches apart onto spray-coated cookie sheets.
Bake at 375°F. for 8 to 12 minutes or until edges are light golden brown. Immediately remove from cookie sheets. Cool completely.
In small bowl, combine all frosting ingredients, adding enough milk for desired spreading consistency; blend until smooth. Spread frosting over cooled cookies.