In 12-inch skillet, melt butter over medium-high heat. Add onions; cook 15 minutes, stirring frequently. If onions are browning too fast, reduce heat to medium. Carefully add 1/4 cup of the water, and stir to deglaze pan. Cook 10 minutes, stirring frequently. Repeat deglazing with remaining 1/4 cup water. Cook 3 to 5 minutes, stirring frequently, until water is absorbed and onions are deeply browned and tender. Stir in 1/2 teaspoon salt; transfer caramelized onions to bowl. Cool 15 minutes at room temperature. Chop onions, and add to small bowl.