In bread machine pan, place dough ingredients in order suggested by the manufacturer. Select "dough" setting on the bread machine. Check dough after 5 minutes of mixing and add water or flour if needed, a Tablespoon at a time.
When cycle is completed, turn dough onto a lightly floured surface. Let dough rest 10 minutes. Mix brown sugar and cinnamon together in a small bowl. Roll dough into a 20x10-inch rectangle. Spread with 3 Tablespoons butter; sprinkle with brown sugar/cinnamon mixture. Roll up jelly-roll style, starting with the long side; pinch the seam to seal. Cut into 20 1-inch thick slices. Place 12 slices, cut side down, into a greased 9x13-inch pan, and the remaining 9 slices in a greased 7x11-inch pan. Cover and let rise in a warm place until doubled, about 45 minutes.
Bake in a 350°F oven for approximately 20 minutes or until golden brown. Cool on a wire rack for 5 minutes before frosting.
In a mixing bowl, beat frosting ingredients until well mixed. Frost warm rolls. Remove rolls from pans and store in refrigerator.
NOTE: The use of the delay timer is not recommended for this recipe.