Lay one of the lobsters on its back. Cut it in half, beginning at the head, down through the natural line between the claws, unfurling the tail as you cut downwards until the lobster can be separated into two. Repeat with the second lobster. Take out the black, thread-like intestine that runs down the tail and the small whitish sac found in the top part of the head. Leave the greenish liver, as this is a great delicacy.
Twist off the big claws. Crack these open with poultry shears, a nutcracker, pestle or rolling pin. Carefully peel away the shell and lift out the firm, white meat, discarding the hard, white, oval membrane that lies in the centre of the claw. Twist off the small claws, taking care not to tear off any lobster meat from the body, and discard.
Scoop out the thick, white tail meat, slice and reserve it. Slowly and carefully remove all the remaining lobster meat from the body, picking it over for stray pieces of shell and bone. Rinse the shells and put them on four serving plates.
Heat the oil in a large frying pan, add the shallots and fry gently for 5 minutes until softened and just beginning to colour. Mix in the anchovies, vermouth and pepper and cook for 2 minutes.
Add the lobster meat and crème fraîche and heat through gently for 3–4 minutes. Stir in lemon juice to taste. Spoon into the lobster shells, sprinkle with paprika and garnish with rocket leaves.