Place dough ingredients in bread machine; set to dough setting. Check after five minutes that dough is slightly sticky but firm to the touch; add flour and water as needed.
For filling: Mix brown sugar and cinnamon together.
After cycle ends, turn out dough onto lightly floured surface. Roll into rectangle to 1/8 inch thickness (It should be about 13 x 9) Brush lightly with butter. Sprinkle on filling, leaving about ½ inch free on far edge. Press filling into dough. Roll tightly into log, pinching at ends. Using a piece of dental floss, cut log in half; cut halves in quarters. Place into greased 9 x 9 (circle or square).
Cover and place in warm area until doubled in volume, about 20 minutes.
Bake at 350 for 20 minutes, or just until browned lightly.
Combine all icing ingredients with whisk. Spread over warm rolls. Cut apart and enjoy!