Place dough ingredients into your bread machine in the order recommended by your manufacturer. Select the dough cycle and run.
Turn out your dough onto a lightly floured surface, cover and let rest for 10 minutes. In a small bowl combine sugar and cinnamon.
Roll the dough into a 16 x 10 inch rectangle. Spread the softened butter evenly over the surface and sprinkle evenly with the sugar/cinnamon mixture.
Roll up the dough, so that your roll is 10 inches long. Cut into 6 rolls. Place rolls in a lightly greased baking pan, cover, and let rise until nearly doubled, about 30 minutes. (It may be hard to see, look more for increase in thickness of the spirals of the roll rather than increase in height)
Preheat oven to 400 degrees, and bake for 15-18 minutes, until the tops are gently browned.
While the rolls are baking, make the icing by whisking together the icing ingredients. Spread the icing over warm rolls before serving.