For filling, combine sugar and cinnamon in a small bowl. Set aside.
Roll dough into a 10"x14"-inch rectangle using a rolling pin. Spread 3 tablespoons butter over dough stopping at least 1/2-inch from the edges on the long side. Sprinkle with cinnamon sugar mixture.
Beginning at long end of the rectangle, roll up tightly to an 18" inch log. Pinch seams to seal. Cut into 9 equal pieces. [TIP: Use unflavored dental floss instead of a knife to cut rolls. To do this, cut a piece of floss about 12 inches long. Slide floss under the roll; bring the ends up and cross over to cut each slice.] Place cut sides down, in greased 9x9-inch baking pan. Cover with a towel; let rise in warm place until doubled in size, about 30 minutes.
Bake in preheated 350°F oven for 25 to 30 minutes or until rolls are golden brown. Cool on wire rack for at least 20 minutes.
Combine all frosting ingredients (start with 2 tablespoons milk and add more if needed) In a large bowl and beat until creamy. Spread over warm rolls.