In a non-stick, 12-inch skillet, melt butter over medium-low heat. Add onions, salt, and cook, stirring occasionally, until onions are very tender and begin to caramelize about 45 minutes.
Transfer onions to a 4.5-quart Dutch oven. Add ½ cup water to the same skillet and heat to boiling, stirring until browned bits are loosened from the bottom of the skillet. Add this liquid to the onions in the Dutch oven.