Step 1To prepare the court bouillon: Pour 4 quarts of water into a large stock pot. Add the bay leaves, parsley, thyme, garlic, black peppercorns, fennel, carrots, leeks, white wine and white wine vinegar. Cover the pot and bring to a boil, then reduce the heat and simmer for 10 minutes. Squeeze in the lemon juice and add the lemon halves. Add sea salt to taste.
Step 2For the shrimp and lobster: For shrimp with the shells intact, pull off and discard the small feet. Use a small pair of scissors to cut a slit down the back of each shrimp, from the head to the last tail segment, cutting into the flesh just slightly. Carefully open the flesh and, using the tip of a knife, remove the dark intestinal tract. Refrigerate, covered, until ready to serve.
Step 3Bring the court bouillon to a rapid boil over medium-high heat, covered. Add the lobster, head first, and return to a boil; boil for 1 minute uncovered. Remove the pot from the heat and add the shrimp. Let stand. Remove the shrimp as soon as they are cooked through: The shells will be pink and the tail meat opaque, 2 to 3 minutes. Remove the shrimp to a tray and refrigerate. Refrigerate for at least 1 hour or up to 24 hours.
Step 4Remove the lobster from the pot (reserving the court bouillon) after it has stood in the court bouillon for 10 minutes. Transfer the lobster to a platter and let cool for about 15 minutes, then refrigerate for at least 1 hour or up to 24 hours. Before serving, pull off each claw. Insert the tip of a large knife between the eyes and cut straight down the length of the lobster to cut it in half.
Step 5For the crab: Bring the court bouillon back to a boil, covered, over medium-high heat. Add the crab. Cover the pot and keep at a low boil. Cook for 4 minutes, then remove from the heat and let the crab stand in the liquid for 30 minutes. Transfer the crab to a platter and cool for 15 minutes. Refrigerate for 1 hour or up to 24 hours. Before serving, clean the chilled crab. Remove the legs (including the knuckle joint) and the claws. Pull off the top shell and remove and discard the feathery gills. Scoop out the yellow matter (to be eaten or discarded) in the crab. Cut the crab in half lengthwise and then each piece in half again crosswise.
Step 6For the mussels, sea snails, periwinkles and cockles: In a saute pan or wide shallow saucepan, add enough court bouillon to come up the sides of the pan about one-half to 1 inch. Bring to a boil and add the mussels, sea snails, periwinkles and cockles. Cover and cook for 1 to 1 1/2 minutes, or until the mussels and cockles have opened. Remove from the heat. Transfer the sea snails and periwinkles to a bowl. Toss the mussels still in the pan with parsley, shallots and sherry vinegar. Remove to a bowl. Let the mussels, sea snails and periwinkles and cockles cool for 15 minutes. Refrigerate, covered, for at least 30 minutes or up to 2 hours.
Step 7Shuck the oysters: Hold an oyster firmly in your hand with a folded cloth towel (the towel will shield your hand should the oyster knife slip). Place the tip of the oyster knife into the hinge of the oyster. Twist the knife to open the hinge; do not force the knife into the oyster. When the hinge pops open, slide the knife sideways halfway into the oyster. Twist the knife again to open the oyster, holding the oyster level so none of the oyster liquor spills out when opened. Use a spoon to gently pry the oyster from the bottom muscle. Continue with the remaining oysters and set aside, each on a half shell, on an ice-lined shallow pan.
Step 8Shuck the clams: Holding a clam in a folded cloth towel, gently slide a small, sharp knife into the front of the clam between the closed shells. Twist the knife to pry the clam open. Gently pry clam from the shell with a spoon. Continue with the remaining clams and set aside, each on a half shell, on an ice-lined shallow pan.
Step 9To prepare the sea urchin: Wearing a glove or using a towel, hold the sea urchin in one hand. Push the tip of a knife or scissors into the top of the sea urchin and cut out a 3-inch circle from the shell. Pour off and discard any liquid inside the sea urchin. Pull out the black parts from inside, leaving the clusters of orange roe. Scoop out the clusters of roe with a spoon, keeping them as whole as possible. Fill the inside of the sea urchin with crushed ice and place the roe on top of the ice to serve.
Step 10Line a platter with shaved or crushed ice and cover with a layer of seaweed. Or arrange parsley and lemon wedges around the platter. Just before serving, remove the tail meat from the lobster and slice into one-half-inch pieces, then return the meat to the shell. You can lightly crack the lobster and crab claws with a crab cracker, if you like. Arrange the shellfish on the platter. Serve with cocktail sauce, mignonette and mayonnaise.