Place all the ingredients for the court bouillon in a large heavy stock pot and simmer for about 15 minutes. Bring to a boil, add the lobster and cook for 4 to 5 minutes. Remove the lobster from the court bouillon and aside to cool and then remove the shell.
Sauté the lobster shells in the olive oil, add the chopped tomatoes, tomato paste, shallots, thyme, bay leaf, carrots, garlic, orange peel and tarragon. Flambé with Cognac, add the white chicken stock and fish stock and cook over low heat for 30 minutes skimming regularly. Add the ginger rounds, infuse for 20 minutes then strain through a China cap sieve. Divide the lobster stock into two portions.
Clarify one half of the lobster stock by mixing the egg whites with the chopped celery and leek. Add a few ice cubes and combine. When the stock has cooled slightly, add the egg white mixture and whisk. Bring to a simmer – but not a boil. Cook over low heat until white foam starts to form on the top of the stock. Once this starts to form, it will take approximately 20 minutes for all of the impurities to rise to the top and form a crust. Place a coffee filter in a china cap sieve over a bowl. Using a ladle and trying not to break the crust, scoop out the consommé leaving the impurities behind, and strain through the coffee filter-lined sieve into the bowl. Mix the agar-agar powder with ¼ of the cooled lobster consommé, bring to a boil; remove from the heat and add to the remaining consommé. Pour into a dish to a 1 to 2 cm layer and refrigerate. Cut out pieces out of the gelled consommé using cutters of various sizes, set aside.
Américaine style sauce:
Add the cream to the remaining lobster stock, reduce slightly then strain. Set aside.
Cook the tapioca pearls in boiling water with the soy sauce for 30 minutes. Drain, add the finely chopped chives, leave cool.
Whisk the egg whites, add sugar and whisk until firm peaks form. Place in a piping bag fitted with a round tip. Refrigerate.
Carefully make an incision along the top of the lobster to make a cavity, fill with the flavored tapioca pearls. Place lobster in the middle of a plate, arrange the consommé cut-outs around it. Pipe the meringue in a decorative curve, like the shape of a comma (optional); use a spatula to spread out. Sift the lobster coral over the top. Drizzle the Américaine style sauce all around.