Use a vegetable slicer or knife to slice the carrots into rounds about ¼ inch thick. Place the carrots in an aluminum or enamel-coated skillet and add the salt, butter, sugar, and water. Cover the top of the skillet with aluminum foil and place the skillet over medium heat. Carefully shake the pan occasionally, taking care that the liquid does not spill out. Continue cooking until carrots are tender and all of the liquid has been absorbed. This should take from 10 to 20 minutes, depending on the heat, the age of the carrots, and the size of the slices. When the carrots are done, remove the aluminum foil and continue cooking briefly until the slices start to turn brown. Sprinkle with chopped parsley and serve.