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1
If using live lobsters, bring a large pot of water to a boil.
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2
Plunge the lobsters in head first and cook over high heat until the lobsters are red almost all over, about 5 minutes.
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3
The water may just have returned to a boil at this point.
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4
Using tongs, transfer the lobsters to a large bowl and let cool.
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5
When the lobsters are cool enough to handle, separate the heads from the bodies.
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6
Using kitchen shears, snip the underside of the tail shells down the center and remove the lobster tail meat in 1 piece.
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7
Remove the dark intestinal vein in the tail, then slice the meat 1/4 inch thick.
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8
Twist off the claws, crack them with a mallet and remove the meat.
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9
Cut the meat from each claw into 3 pieces.
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10
Cover and refrigerate the lobster meat if not making the recipe straight through.
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11
Reserve the lobster shells, including the heads.
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12
Rinse the insides of the lobster shells, then break them up into very small pieces.
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13
In a large saucepan, heat the pure olive oil.
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14
Add the lobster shells and cook over moderately high heat, stirring often, until the shells start to brown, about 5 minutes.
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15
Add the shallots and thyme sprigs and cook, stirring, until the shallots start to brown, about 3 minutes.
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16
Reduce the heat to moderate and add the tomato paste.
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17
Cook, stirring, until the tomato paste starts to stick to the bottom of the pan, about 3 minutes.
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18
Add the Cognac and simmer, scraping up the browned bits from the bottom.
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19
Add the water and a pinch of salt and bring to a simmer.
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20
Cook the lobster stock over low heat until reduced to 2 cups, about 20 minutes.
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21
Skim the lobster oil from the surface and discard.
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22
Line a fine strainer with 4 layers of dampened cheesecloth and slowly strain the lobster stock through it into a clean large saucepan.
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23
Put the porcini in a heatproof bowl.
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24
Bring 2 cups of chicken stock to a simmer and pour over the porcini; let the mushrooms soften for 20 minutes.
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25
Rub the porcini to loosen any grit, then lift them out.
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26
Reserve the porcini for another use.
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27
Let the soaking liquid stand for 5 minutes so the grit falls to the bottom, then pour the liquid into the pan with the lobster stock, leaving behind any grit.
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28
Add the remaining 6 cups of chicken stock to the saucepan.
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29
Bring the broth to a bare simmer.
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30
Season with salt and white pepper and keep warm over very low heat.
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31
Bring the lobster meat to room temperature if needed and season lightly with salt.
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32
Spoon the lobster into 10 warmed shallow soup plates.
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33
Ladle the broth over the lobster meat and garnish with a few chervil leaves.
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34
Drizzle with extra-virgin olive oil and serve.
