Rub butter over the fish, and sprinkle with salt and pepper. Place the darn in a well-buttered casserole or oven-proof braising dish. Sprinkle over, under and around it the onion, garlic, 3 tablespoons of parsley, thyme and crushed bay leaf Add the mushrooms around the sides. Pour the wine over all, to less than midway up the side, and then cover the darn loosely with a sheet of buttered aluminum foil.
In an oven preheated to 400°F cook the dish for 10 minutes per inch of thickness or longer, basting frequently. When done the fish will have reached an internal temperature of 140°F. Remove the aluminum foil, baste, and cook 10 minutes longer as the fish skin takes on a dark, variegated color. Add wine as necessary to keep the fish moist. Remove the fish to a hot platter, and keep warm while the sauce is prepared.
Strain the cooking liquid through a fine sieve, add the fish stock and up to another cup of burgundy wine to make a total of 1½ cups. In a saucepan over high heat, reduce this to about 1 cup, then add 5 tablespoons butter, whisking to a rich, frothy, thick sauce. Adjust the seasonings with salt and pepper, and pour a few tablespoons of the sauce over the fish. Add the remaining parsley and pour the rest of the sauce into a sauce boat. Serve with the mushrooms, glazed pearl onions and additional parsley.