Melt half the butter in a pan, add the scallions and onion and cook for 5 minutes until soft but not coloured. Add the carrot and cook for 2 minutes. Add the lobster halves, fish stock, parsley, bay leaf, peppercorns and the water. Bring to a boil, reduce the heat and simmer for 20 minutes, skimming the surface as required.
Remove the lobster from the stock, cool slightly and take the meat from the shells. Set the lobster meat aside, crush the shells and return them to the pan. Continue simmering for a further 40 minutes. Strain the stock, then strain again through a sieve lined with 2 layers of damp muslin or cheesecloth.
Cut some thin slices from the lobster to use as a garnish and set aside. In a blender, blend the remaining lobster flesh with a little of the strained stock until smooth. Mix the flour and remaining butter to a paste. Add the pureed lobster to the pot along with the flour paste, tomato puree, sherry, cream, nutmeg and salt and pepper to taste. Mix well.
Add the tarragon and the remaining stock and cook, stirring continuously, over high heat until the soup boils and thickens. Reduce the heat and simmer gently for 5 minutes. Season to taste and serve garnished with the reserved lobster and some sprigs of tarragon, if desired.