Place the water, oil, dry milk powder, 3 1/2 tablespoons sugar, salt, flour, and yeast into a bread machine in the order recommended by the manufacturer. Run the machine on the Dough cycle. At the end of the cycle, remove the dough and place it on a floured work surface.
Mix 1/3 cup of sugar with the cinnamon in a bowl, and set aside. Spray a 9x13 inch pan with cooking spray.
Roll the dough out into a 10x15 inch rectangle. Spread the softened butter over the dough and sprinkle evenly with the sugar-cinnamon mixture. Roll up the dough from the long side into a tight roll. Cut the roll into 12 slices about 3/4 inch thick and place the slices into the prepared baking pan with the rolls barely touching each other. Cover with a cloth, and let rise in a warm place until doubled, 30 to 60 minutes.
Preheat oven to 375 degrees F (190 degrees C).
Bake the rolls in the preheated oven until the tops of the rolls are golden brown, 15 to 20 minutes.