Preheat oven to 375 degrees F. Preheat a grill to high heat.
To make the fish: fillet the fish and remove all bones (You can ask your fishmonger to do this). Season the fish with the olive oil, and salt and pepper. Grill on both sides until the fish has clear grill marks, about 6 minutes per side. Remove from the grill, place on a sheet pan, and finish in the oven.
Transfer to a warmed platter and brush with Herbed Butter Sauce.
To make the sauce: in a small pan, sweat the shallots in butter. Add the wine, stock, vinegar, and lemon juice and simmer until reduced by half.
Stir in 3 tablespoons cream. Add half of the tarragon. Whisk in the cold butter, 1 tablespoon at a time, strain and add remaining tarragon and chopped parsley. Season with salt and pepper to taste.