Combine the yeast, 1/2 tsp. of sugar and warm water in a small bowl. Stir and set aside. In the bowl of a stand mixer, combine the milk, 1/3 cup sugar, melted butter, salt and eggs. Stir in the yeast mixture. Gradually add the flour, one cup at a time, and beat until a sticky dough forms.
Preheat oven to 200 degrees. Dump the dough out onto a floured surface and knead 5-7 minutes, until smooth. Place in a buttered bowl and cover loosely with a damp towel. Turn the oven off. Place the bowl in the warm oven for 45 minutes, until the dough is doubled in size.
Meanwhile, prepare the filling: Combine the cinnamon and 1/2 cup sugar and melt 1/2 stick of butter.
Punch the dough down and roll out on a floured surface. Form a rectangle measuring 13x19 inches. Brush with melted butter and sprinkle generously with cinnamon-sugar mixture. Start rolling from the long end, jellyroll style. Cut into 15 pieces.
Melt the other 1/2 stick of butter pour into a 9x13 baking dish. Coat well. Sprinkle the remaining 1/4 cup sugar. Place the rolls in the pan, making sure there is a little space between them. Cover with a dish towel and let rise for 45 minutes.
Preheat oven to 350 degrees. Cover the pan loosely with foil and bake 25 minutes. Remove the foil and bake another 15-20 minutes.
While the rolls are baking, combine all frosting ingredients except for the water in a small bowl. Add the water, one tablespoon at a time, until desired consistency is reached. Spread frosting over warm rolls.