Cut out any bones that may remain in the fillets. Mix the soy sauce and sugar in a resealable plastic bag and add the fillets. Seal the bag and toss it a bit to evenly distribute the marinade. Refrigerate for at least 4 hours, or as much as 24 hours.
Toss panko or bread crumbs with parsley, thyme, and melted butter in a mixing bowl.
When ready to assemble, preheat oven to 350F. Lift the fillets from the marinade and arrange in baking dish, skinned side down. Top each piece with an even coating of the crust mixture, gently patting it on with fingertips. Bake for 25 to 30 minutes, or until fillets flake apart when nudged. Turn the broiler to high and broil until the crumbs are golden brown.