How to Make It
Heat the olive oil in a small stockpot. Add the fish heads and bones, leeks, shallot, celery and the thyme and parsley sprigs. Cook over moderate heat, stirring occasionally, until the fish bones turn white and the vegetables and herbs are fragrant, about 4 minutes.
Add the wine and cook for 1 minute. Add the water, tomato, bay leaf and a large pinch of salt and bring to a simmer over moderately high heat. Skim any foam that rises to the surface and reduce the heat to low. Simmer the stock for 20 minutes, skimming often.
Slowly pour the stock into a fine strainer set over a saucepan, leaving the solids at the bottom of the stockpot. You should have 4 cups; if not, simmer the strained stock until it has reduced to 4 cups.
In a medium saucepan, bring 1 inch of water to a boil. Add the clams, cover and cook over high heat until they open, about 3 minutes. Using tongs, transfer any opened clams to a bowl. Cover and continue until all of the clams have opened. Reserve the liquid in the saucepan.
If using live lobsters, bring a large pot of water to a rolling boil. Add the lobsters, cover and cook for 12 minutes, then drain and let cool slightly. Twist off the tails and remove the claws. Crack the claws and remove the meat. Using kitchen shears, cut down 1 side of the tails and remove the meat from the shells in 1 piece. Make a thin cut down the center of the outside of the tails and remove the intestinal veins. Cut the tails crosswise into thick medallions.
In a large enameled cast-iron casserole, cook the onion in the 1/2 cup of olive oil over moderately low heat until translucent. Add the garlic and cook for 2 minutes longer. Add the tomatoes and cook over moderate heat for 20 minutes, stirring occasionally. Stir in the wine and bring to a boil; simmer for 2 minutes. Pour in the fish stock. Add the reserved clam cooking liquid, stopping before you reach the sediment at the bottom. Bring to a boil, then reduce the heat and simmer for 15 minutes. Season the mixture with salt and black pepper and add the crushed red pepper.
Add the monkfish to the casserole and gently stir it in. Cover and simmer for 3 minutes, then add the shrimp and squid. Cover and cook until the squid is just tender, 2 to 3 minutes. Add the reserved clams and lobster meat and cook just until all of the seafood is heated through. Stir in the chopped parsley.
Put a piece of toast in the bottom of each soup plate and ladle the fish stew on top, making sure that each serving includes some of each variety of seafood. Sprinkle the stew with parsley and serve as soon as possible.