Gather your ingredients together.
From the soft side of the shell, cut the lobster tail(s) in half lengthwise.
Melt half the butter in a pan, add the scallions and onion and cook for 5 minutes, or until soft.
Add the carrots and cook for 2 minutes.
Add the lobster halves and cook for 3-5 minutes.
In a large soup pot add the fish stock, parsley, bay leaf, peppercorns, and water.
Add the lobsters to the stock pot and bring to a boil, reduce the heat and simmer for 20 minutes, skimming the surface as required.
While the pot is simmering cut the tomatoes into quarters and puree in a blender.
Remove the lobsters from the stock, cool slightly and remove the meat from the shells.
Cut 4-6 thin slices from the lobster to use as a garnish and set aside.
Set the lobster meat aside, crush the shells and return to the pan. Continue simmering for an additional 40 minutes.
Strain the stock, with 2 layers of damp muslin or cheesecloth.
In a blender, blend the remaining lobster flesh with a little of the tomato puree until smooth.
In a separate pan, 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. If the soup is too thin cook down until you get the desired thickness.
Season to taste and serve garnished with the reserved lobster and some sprigs of tarragon, if desired.