Rinse fish and pat dry. Set fish, skin down, on a sheet of heavy foil and trim foil to make a rim about 2 inches wider than fish. Fold excess foil up to create a lip around fish.
In a bowl, combine butter, wine, lemon juice, and soy sauce.
Prepare barbecue for indirect heat.
If using charcoal briquets, mound and ignite 60 briquets on the firegrate of a barbecue with a lid. When briquets are dotted with gray ash, in 15 to 20 minutes, push equal amounts to opposite sides of firegrate. Add 5 more briquets to each mound of coals. Set a drip pan on firegrate between coals.
If using a gas barbecue, turn all burners to high and close lid for 10 minutes. Adjust burners for indirect cooking (no heat down center) and keep on high.
Set fish, foil down, on grill but not over heat source. Brush fish generously with butter mixture, then again about every 5 minutes, until fish is opaque but still moist-looking in center of thickest part (cut to test), 20 to 30 minutes. Cover grill (open vents for charcoal).
Slide a large, rimless baking sheet under foil, then slide fish from pan onto a platter. Sprinkle with parsley. Cut fish into portions and lift from skin. Season with juice from lemon wedges.