This bouillabaisse combines spiny lobsters, snapper, Gulf shrimp and mussels in a light, spicy broth.
Fill a tall stockpot with water; bring to a boil. Add lobsters, and cook 9 minutes. Remove lobsters from water; set aside until cool enough to handle. Separate claws and tails from bodies; set all parts aside.
Make a bouquet garni by placing thyme sprigs, bay leaves, 10 parsley sprigs, and peppercorns in a 12-inch-square piece of cheesecloth. Form a bundle, and tie with kitchen twine. Set bouquet aside.
In a wide, low-sided stockpot, combine 1 tablespoon butter and 1 1/2 tablespoons olive oil; melt over low heat. Add the shallots and garlic; cook until vegetables are translucent, about 10 minutes. Meanwhile, remove and discard the peel and pith from limes; cut the flesh in half, and set aside. Transfer the shallot mixture to a small bowl, and set aside.
Place lobster bodies in the wide stockpot. Raise the heat to medium, and cook, stirring constantly, 3 to 4 minutes. Add the lime flesh and Pernod; light a long wooden match, and carefully ignite Pernod. Allow the flame to burn out. Add saffron; cook 1 minute more. Add tomato paste, bouquet garni, and fish stock. Raise heat to high, and bring to a boil. Reduce heat, and let stock simmer, skimming foam as it rises to the surface, until stock is reduced by one-third, about 40 minutes. Set a cheesecloth-lined sieve over a large bowl, and strain stock; set aside. Discard solids, and rinse stockpot.
Using kitchen shears, cut open a lobster tail, and carefully remove the meat in one whole piece; set aside. Repeat with remaining tails, and slice meat in half lengthwise. Crack or cut open each claw, removing meat in one piece. Discard shells, and set the meat aside, covered.
Heat the remaining tablespoon olive oil in a large nonstick skillet over high heat. Working in batches, cook the snapper fillets until browned and crisp, 3 minutes on each side. Transfer fillets to a plate, and set plate aside in a warm place.
Melt the remaining 1/2 tablespoon butter in the rinsed stockpot over medium-high heat. Add the reserved shallot mixture, shrimp, and mussels; saute 4 minutes. Add strained stock, Tabasco, and salt; simmer 3 minutes. Add reserved lobster meat; cook until mussels open and shrimp have cooked through, about 2 minutes. Remove from heat.
To serve, place a snapper fillet in each of six large soup plates, and evenly distribute the shellfish and broth among the bowls. Coarsely chop the remaining 6 sprigs of parsley, and garnish bouillabaisse.
Pernod is an anise-flavored liqueur.
The 6 spiny lobsters can be replaced with 4 one-and-a-half pound Maine lobsters. The large Gulf shrimp can be replaced with prawns.