Melt butter in a skillet over low heat. Add onions and cook slowly, up to 45 minutes to release maximum flavor, or until nicely browned, stirring frequently. Transfer to a slow cooker. Add water, bouillon, Worcestershire sauce, and salt. Cover and cook on low for 4 to 6 hours.
To serve, top each bowl with 1 slice of bread. Sprinkle each with 2 tablespoons Parmesan. Recipe may be doubled and kept hot in slow cooker.