In a small bowl mix water, yeast, and 1 tablespoon sugar and set aside to proof. Mix together milk, sugar, melted butter, salt, and eggs. Add yeast mixture and 4 cups of flour to mixture beat until smooth. Stir in more flour until dough comes away from the side and forms a ball. Mix for 8 minutes to knead, you may also knead it by hand. Cover and let rise until it doubles in size. Roll dough out onto a floured surface into a 15 x 20-inch rectangle. Spread softened butter all over dough and sprinkle with sugar then cinnamon. Roll up dough tightly and cut into about 1 1/2-inch slices using thread or unflavored dental floss. Place cinnamon rolls slices close together in buttered 9 x 13-inch pan cover pan and allow to rise in a warm place for about 1 hour. Bake rolls in a 350 degress oven for 25 to 30 minutes, or until golden brown. Frosting: Mix together last 4 ingredients until smooth and frost when rolls have almost cooled. Yum!