Stir the yeast into the warm water in a large mixing bowl and let stand a few minutes to dissolve. Add the potato water, mashed potato, 1/2 cup sugar, salt, butter and egg and beat well. Add 2 cups of the flour and beat until smooth. Add enough of the remaining flour to make a manageable dough, then turn out onto a lightly floured surface and knead for 1 minute or 2. Cover with plastic wrap to prevent drying out. Let rest 10 minutes. Resume kneading for about 8 to 10 minutes until the dough is smooth and elastic. Sprinkle on a little more flour as necessary to keep dough from being too sticky. Place in a large greased bowl, cover and let rest until double in bulk.
Punch dough down. On a floured surface, roll dough into a 14-by-8-inch rectangle. Spread dough with 1/2 cup softened butter. Mix 2/3 cup sugar with 1 tablespoon ground cinnamon in a small bowl. Sprinkle over butter. Roll up from long sides like a jelly roll. Cut into 12 equal pieces. Arrange, cut sides up, in a greased 9-by-13-inch pan. Cover pan loosely with plastic wrap and let rise until doubled in bulk approximately 30 to 40 minutes. Bake at 350 degrees for 30 to 40 minutes or until done. Remove from oven and cool on wire racks. Drizzle with both icings 1 at a time.
Combine all ingredients to icing of drizzling consistency.
Combine all ingredients to make icing of drizzling consistency.