Combine potatoes, potato water, butter, sugar, salt and hot water in large mixer bowl. Stir until butter melts; set aside and let cool. Combine yeast and 1/2 cup warm water in small bowl. Add eggs, 2 cups flour and yeast mixture to potato mixture. Continue adding flour, 1 cup at a time until soft dough forms.
Knead on a lightly floured surface until smooth and elastic (about 4 to 6 minutes), OR knead with electric mixer using dough hook. Place in a greased bowl, turning to coat. Cover and let rise in a warm, draft-free place about 1 hour, until doubled.
Punch dough down; divide in half. Roll one portion of dough on a lightly floured surface to a 12x18-inch rectangle. Spread with half the butter. Combine sugar and cinnamon; sprinkle half of the mixture over surface. Roll up tightly, sealing edges. Cut into 12 slices. Place in greased 13x9-inch pan.
Repeat with remaining dough. Cover and let rise 30 to 45 minutes.
Bake in preheated 350 degrees F oven for 25 to 30 minutes. Cool for 15 minutes. Combine icing ingredients and drizzle over rolls.