Melt butter in heavy sauté pan over medium heat. When melted, add onions and sauté for 3 minutes. Stir in currants, brown sugar and vinegar. Cook, stirring constantly, for about 4 minutes or until sugar has completely dissolved. Add beans. Lower heat to a minimum flame. Cover and cook for about 5 minutes.
Toss beans to coat. Taste. If the sweet/sour flavor seems well balanced, remove from heat. If not, add sugar or balsamic vinegar, whichever is necessary, a bit at a time, until balance is reached. Serve hot or at room temperature. Serves 6.