Combine first 4 ingredients in a 14-quart stock pot. Bring to a boil. Cook 5 minutes; remove scum. Add cabbage, spinach, lettuce, salt, peppercorns, and mace. Bring to a boil. Reduce heat; simmer, uncovered, 4 hours. Remove from heat; cool slightly, and strain broth through cheesecloth. Reserve beef, veal, and hen for other uses. Cover and chill broth thoroughly; skim and discard fat from broth, setting broth aside.
Sauté skirt steak in butter in a medium skillet until browned. Add 1/2 cup broth; cover and simmer 10 minutes or until tender.
Heat remaining broth thoroughly. Stir in steak mixture. Spoon into individual serving bowls. Serve immediately.