Scale fish by placing it in the sink under cold running water. Grasp the fish firmly by the gills and scrape off scales with a fish scaler or small, dull knife. Using short strokes, work from the tail to the head.
To remove the head, cut the flesh on both sides with a knife. If the fish is small, slice directly through the spine. For a larger fish, place the knife between vertebrae and tap the back of the knife with a hammer.
To fillet, use a sharp, thin knife. With the tilefish lying on its side, insert the knife behind the gills, and cut in an arc down to just above the backbone. Continue cutting parallel to the backbone toward the tail. Bring the knife up at the tail and remove the fillet.
The secret to successful tilefish cookery is to not overcook it. Whichever of the following cooking methods you choose, your tilefish will be cooked when its flesh becomes opaque yet is still moist on the inside.
Place tilefish fillets or chunks in a greased baking dish (or wrap in oiled foil) and place on a baking sheet. Brush with melted butter or oil and season with salt and pepper, or cover with a piquant sauce. Bake in a preheated 450°F (230°C) oven 10 minutes per inch (2.5cm) of thickness.
Place marinated tilefish fillets on perforated foil on a grill over hot coals. Baste frequently and turn once halfway through cooking period. Because tilefish is lean compared to other protein foods, it does not exude a lot of self-basting fat. Be sure all grills, baskets, racks, and foil, are well-oiled to ensure easy handling of tilefish while barbecuing. Marinating and frequent basting will keep tilefish moist and flavorful.
Place fillets on well-greased baking pan. Pour enough stock in pan to cover the bottom of the pan. Brush top with butter or oil. Broil under preheated broiler 4 to 5 inches (about 10 to 12.5cm) from heat. Do not turn, but baste several times. Cook until opaque and moist on the inside, 6 to 10 minutes.
Coat tilefish with seasoned flour or crumbs and fry in a small amount of hot butter or oil, turning once halfway through cooking time.
Pour oil into a wok or deep fryer; it should be at least 1 1/2 inches (about 3.8cm) deep, and the cooker should be less than half full of oil. Heat oil to 375°F (190°C), using a thermometer to monitor temperature. Cut tilefish into similar sized pieces, 1 1/4 to 1 1/2-inch (about 3.2 to 3.8cm) thick. Dip in batter, drain, then slip fish into hot oil. Cook until brown, 2 to 3 minutes.
Bring poaching liquid, consisting of water, broth, and herbs and spices, to a simmer. Slip in tilefish fillets, then cover pan and keep liquid at a simmer for about 8 minutes per inch (2.5cm) of thickness.
Place tilefish fillet on a greased perforated rack over 1 to 2 inches (about 2.5 to 5cm) of rapidly boiling water. Cover with a tight-fitting lid and keep water at a constant boil through cooking time.