In a large casserole combine octopus, carrots, celery, onion, bay leaves, salt, pepper, thyme, red wine and water. Bring to a slow boil and simmer 45 minutes, or until octopus is very tender when pierced with a fork. Remove from heat and let octopus cool in its broth.
Set aside 1 1/3 cups of broth for sauce. When octopus is cool enough to handle, remove it from broth and rub it well to remove purplish skin. Rinse tentacles in broth as they are cleaned. Drain octopus and transfer to a large bowl.
Make marinade: in a small bowl combine marinade ingredients. Pour over octopus and toss to coat. Marinate, covered and refrigerated, for at least 24 hours, and up to 3 days.
Make sauce: in a small saucepan combine strained reserved broth, olive oil, lemon juice and vinegar. Reduce by half over high heat. Remove pan from heat and whisk in butter, 1 tablespoon at a time. Stir in parsley. Keep warm.
Prepare a charcoal broiler. Drain tentacles and pat dry. Grill 4 minutes, turning frequently, until lightly charred and heated through. Serve 2 tentacles per person, with sauce spooned over, garnished with parsley and lemon wedges.
Recipe courtesy of Charles Bowman, Periyali Restaurant, New York