Score both sides of steak in a diamond pattern by making shallow diagonal cuts at 1-inch intervals. Place meat in a large resealable plastic bag set in a shallow dish. For marinade, in a small bowl combine the 1/3 cup wine vinegar, the onion, oil, Worcestershire sauce, the 2 cloves garlic, and the dry mustard. Pour marinade over meat; seal bag. Turn to coat meat. Marinate in the refrigerator for at least 6 hours or up to 24 hours, turning bag several times.
For sauce, in a medium saucepan cook green onion in 2 tablespoons hot butter over medium heat until tender. Stir in the flour and thyme. Stir in broth and wine. Bring to boiling, stirring occasionally; reduce heat. Boil gently, uncovered, for 15 to 20 minutes or until reduced to about 1 cup. Keep warm.
Drain meat, discarding marinade. Pat meat dry with paper towels. Preheat broiler. Place steak on unheated rack of a broiler pan. Broil 3 to 4 inches from the heat for 15 to 18 minutes or until medium doneness (160 degrees F), turning once. Slice steak thinly across the grain.
Meanwhile, combine zucchini, carrot, and the 1 clove garlic; place in a steamer basket over boiling water. Steam about 4 minutes or just until tender. Transfer to bowl. Stir in the 1 tablespoon butter and the walnuts. Season to taste with salt and pepper.
To serve, spoon some of the sauce over meat; pass the remaining sauce. Serve the zucchini and carrot mixture with the meat. If desired, garnish with fresh herb sprigs.