In a large, heavy saucepan, melt butter on medium heat until foam subsides, then raise heat to high and stir in apples and 1/4 teaspoon salt. Cook, stirring frequently, until apples begin to breakdown into something like applesauce, about 15 minutes. Reduce heat to medium and continue to cook until apples become a relatively smooth sauce that can be dragged across the bottom of the pan with a wooden spoon. Add 1/4 cup sugar, increase heat to high, and cook until apples turn a dark caramel color, 2 to 3 minutes. Stir frequently to avoid burning.
