DO-AHEAD TIP: Marinate fish for 30 to 60 minutes (see recipe).
Place fish in a large zipper-topped plastic bag. In a small bowl, combine next 8 ingredients (garlic through salt). Pour mixture over fish.
Seal bag and refrigerate for 30 to 60 minutes. Preheat grill to MEDIUM-HIGH and lightly oil the grate.
Grill fish for 10 minutes per inch of thickness or until opaque, basting frequently with marinade. Garnish with chopped parsley if desired, serve, and enjoy!