Rinse and pat dry the reserved fish carcass, set aside. Preheat the fryer. Season the flour with salt and pepper. Dredge the carcass in the seasoned flour, on both sides, reserving the flour. Shake off any excess flour. Fry the carcass until golden brown, about 2 to 3 minutes. Remove from the oil and drain on paper towels. Season with salt and pepper. Cut the fillets into 2 ounce pieces. Season with salt and pepper. Dredge the fillets in the reserved flour, coating completely. In a large saute pan, over medium-high heat the oil. When the oil is hot, but not smoking, lightly pan-fry the fish for 1 minute on each side. Remove from the pan and set aside. In the same saute pan, add the shallots and garlic. Season with salt and pepper. Saute for 1 minute. Add the mushrooms. Season with salt and pepper. Saute for 1 minute. Add 1 3/4 cup of the chicken stock. Dissolve the cornstarch in the remaining stock, making a slurry. Bring the stock to a boil. Stir in the slurry. Boil the liquid for 2 minutes and then reduce to a simmer. Add the fish fillets and simmer for 3 to 4 minutes. Reseason and stir in the parsley. To assemble, place the fried fish carcass on a large platter. Lay the fillets over the crispy bone. Spoon the sauce over the fillets. Serve immediately.
Dish from Sun Lee Place in New York City