Combine potatoes, potato water, butter, sugar, salt and hot water in large mixing bowl. Stir until butter melts; set aside and let cool. Combine yeast and 1/2 cup warm water in small bowl. Let rest 5 minutes. Add eggs, 2 cups flour and yeast mixture to potato mixture. Beat until well mixed. 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.
Let rise in a warm, draft free area about 1 hour, until doubled in size. Punch dough down; divide in half.
Roll one portion of dough on a lightly floured surface to a 12 x 18-inch rectangle. Spread with half the butter mixture (I use my hands). You may also wish to add a little more butter to the mixture if you have difficulty spreading or warm up in the microwave for a couple of seconds. Roll up tightly lengthwise, sealing edges. Cut into 12 slices. Place in greased 13 x 9-inch pan. Repeat with remaining dough. Cover.
Let rise 30 to 45 minutes until nearly doubled.
Bake in preheated 350 degrees F oven for 25 to 30 minutes.
Cool for 15 minutes. Combine icing ingredients and drizzle over rolls.