Mix sugar, shortening, egg, molasses and water. Stir in remaining ingredients except frosting. Cover and refrigerate at least 1 hour.
Heat oven to 400 degrees. Drop dough by rounded teaspoonfuls about 2 inches apart onto ungreased cookie sheet. Bake until almost no indentation remains when touched, about 8 minutes. Immediately remove from cookie sheet. Cool; frost with Vanilla Butter frosting.
Vanilla frosting:
Mix 1/4 cup butter, softened, and 2 cups powdered sugar. Beat in about 1 tablespoon milk and 1 teaspoon vanilla until smooth and of spreading consistency.