In a mixing bowl, combine sugar, molasses and coffee. Combine dry ingredients; add to sugar mixture and mix well. Refridgerate for 2 hours. Roll dough on a floured surface to about 1/4 inch thickness. Cut with 3-inch cookie cutters. Place on baking sheets that have been coated with non-stick cooking spray. Bake at 350° for 8-10 minutes or until set. Cool on wire racks. Meanwhile, for frosting, combine sugar, water and vinegar in a heavy saucepan. Cover and bring to a boil. Uncover and cook over medium-high heat until a candy thermometer reads 234-240° (soft ball stage), about 5-10 minutes. Remove from heat; stir in marshmallows until smooth. In a mixing bowl, beat egg whites until frothy. Gradually beat in sugar mixture; beat on high for 7-8 minutes or until stiff peaks form. Frost the cookies.