The secret to successful monkfish cookery is to not overcook. Whichever of the following cooking methods you choose, your monkfish will be cooked when its flesh becomes opaque but is still moist on the inside.
When preparing monkfish, peel off the black skin with a paring knife, then pull off the thin silver membrane. To fillet, lay the tail on a board and slide a knife along next to the backbone.
Place monkfish 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 sauce made of liquid, herbs, spices, and vegetables. Bake in a preheated 450°F (230°C) oven.
Cut monkfish into cubes and place them directly on a greased grill, 4 to 6 inches (about 10 to 15cm) above prepared coals or fire. Baste with butter, oil, or marinade and close hood of grill. Cook until fish is opaque and moist on the inside, 6 to 8 minutes.
Place seasoned monkfish on well-greased broiler pan and brush with butter or oil. Broil under preheated broiler 4 to 5 inches (about 10 to 12cm) from heat, until fish is opaque and moist on the inside.
Coat monkfish 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 monkfish into similar-sized cubes. Dip in batter, drain, then slip pieces into hot oil. Cook until brown, about 2 to 3 minutes.
Bring poaching liquid, consisting of water, broth, herbs, and spices, to a simmer. Slip in monkfish, then cover pan and keep liquid at a simmer for about 8 minutes per inch (about 2.5cm) of thickness.
Place monkfish 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. Steam 5 to 10 minutes for fillets 1-inch (2.5-cm) thick or less; 15 to 20 minutes for 2-inch (5-cm) thick fillets.