Preheat oven to 400 degrees F.
Roll out dough on a lightly floured surface to form a 15 by 7-inch rectangle. In a small bowl, combine brown sugar and cinnamon. Set aside. Spread 2/3 cup softened butter over dough and then evenly sprinkle with cinnamon-sugar mixture. Starting at the long edge, roll up dough as for a jelly roll. Cut roll into 16 slices and then set aside in a warm place and allow dough to rise until doubled in size, about 1 hour.
Divide rolls among 2 lightly buttered round baking pans. Bake for 15 minutes or until golden on top. While the rolls are baking, combine the icing ingredients with an electric mixer until fluffy. Frost the warm rolls with the icing. Serve warm.