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1
In a large soup pot, melt 4 tablespoons of the butter over medium heat and add the carrots, shallots and celery.
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2
Cook, stirring, until the vegetables are very soft, about 5 minutes.
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3
Set aside.
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4
Place a cutting board inside a sheet pan.
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5
(This will catch all the juices from the lobsters.)
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6
Lay a lobster on the cutting board.
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7
Place the tip of a large, heavy knife at the indentation where the carapace meets the head of the lobster, making sure that the cutting blade is facing toward the lobster's eyes.
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8
Swiftly and forcefully, plunge the knife through the lobster until the point of the knife hits the cutting board.
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9
Immediately force the blade down, splitting the head of the lobster.
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10
(The lobster will be dead, although it may still move.)
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11
Repeat with the remaining lobster.
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12
Twist off the tails and claws of the lobsters.
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13
Split the bodies in half and scoop out and discard the spongy green parts in the head.
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14
Put the lobster pieces and any juice that has accumulated in the sheet pan into the pot with the vegetables and cook, stirring, over medium-high heat until the shells are bright red, 8 to 10 minutes.
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15
Remove the lobsters from the pot and cool a few minutes.
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16
Remove the meat from the claws and tails and refrigerate.
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17
Chop the shells into small pieces and return them to the pot.
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18
Cook the shells for a few minutes over high heat.
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19
Add 4 tablespoons of the Cognac and ignite it.
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20
When the flames die, add wine, stock, tarragon leaves, bay leaf, tomatoes, 1 teaspoon of salt and a few grinds of pepper.
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21
Lower the heat and simmer for 45 minutes.
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22
Remove as many large pieces of shell as possible and place them, a cup or two at a time, in a food processor.
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23
Pulse until the shells are finely ground.
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24
Return ground shells to the pot and add the rice and 3 cups of water.
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25
Dice the meat from the tails only and add it.
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26
Cover the pot and simmer another 30 minutes.
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27
Put the soup through a food mill.
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28
Discard the solids and strain the puree through a fine sieve.
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29
Put the puree in a large saucepan and add the cream, milk and remaining Cognac.
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30
Heat very gently, not allowing it to boil, until hot.
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31
Just before serving, whisk in the remaining tablespoon of butter.
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32
Ladle soup into bowls and chop the claw meat to use with a little chopped tarragon for garnish.
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33
Serve immediately.
