Combine onion, parsley, vinegar, oil, mustard, garlic and thyme. Remove any visible fat from the beef chuck shoulder steak and place steak in plastic bag. Add marinade, spreading evenly over both sides.
Close bag securely and marinate in refrigerate 6 to 8 hours (or overnight, if desired), turning at least once. Pour off marinade and discard.
Place steak on rack in broiler pan so surface of meat is 3 to 4 inches from heat. Broil 16 to 18 minutes to desired doneness (rare to Medium-rare), turning once. Carve steak into thin slices to serve.
Cajun Country -- New Iberia, Louisiana