Combine onion, parsley, vinegar, oil, mustard, garlic and thyme.
Place beef chuck shoulder steak in plastic bag; add onion mixture, spreading evenly over both sides.
Close bag securely; marinate in refrigerator 6 to 8 hours (or overnight, if desired), turning at least once.
Pour off marinade; discard.
Place steak on rack in broiler pan so surface of meat is 3 to 5 inches from heat source.
Broil about 16 minutes for rare and about 18 minutes for medium, turning once.
Carve steak diagonally across the grain into thin slices.
Garnish as desired.