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1
Bring a large pot of water to a boil.
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2
Add the lobsters, head first, and cook for 5 minutes.
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3
The water may not come back to a boil, but the lobsters will be almost cooked through.
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4
Using tongs, transfer the lobsters to a large rimmed baking sheet to cool.
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5
Reserve 3 cups of the cooking liquid.
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6
Crack the claws and knuckles and remove the meat.
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7
Using scissors, cut along the inside of the tail shells and remove the meat.
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8
Remove and discard the dark intestinal veins from the tails.
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9
Put all of the lobster meat in a bowl and refrigerate.
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10
Remove the dark-green eggs from the bodies and top of the tails and reserve.
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11
Using poultry shears, cut the shells into 2- to 3-inch pieces.
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12
In a large saucepan, heat the vegetable oil.
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13
Add the lobster shells and cook over high heat, stirring, until they are sizzling and just starting to brown, about 5 minutes.
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14
Add the shallots and thyme and cook over moderately high heat until the shallots soften, about 4 minutes.
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15
Add the tomato and cook until the juices evaporate.
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16
Add the wine and boil until reduced by half, about 4 minutes.
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17
Add the reserved 3 cups of lobster cooking liquid and bring to a boil.
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18
Simmer over moderately low heat until reduced to 3 cups, about 20 minutes.
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19
Strain the lobster broth through a fine sieve and return it to the saucepan.
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20
Bring the lobster broth to a simmer over moderately high heat.
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21
Put the reserved lobster eggs in a small sieve that fits in the pan of lobster broth and simmer until they turn bright red, about 1 minute.
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22
Remove the sieve from the broth and press the eggs through the mesh into a small bowl to separate them.
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23
Return the lobster broth to a boil, add the heavy cream and boil over high heat until reduced to 1 cup, about 7 minutes.
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24
Reduce the heat to low.
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25
Slice the lobster tails 1/3 inch thick.
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26
In a large pot of boiling salted water, cook the pappardelle, stirring, until al dente.
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27
Drain the pasta and return it to the pot.
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28
Add 1 tablespoon of the butter, toss well and cover.
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29
Add the lobster meat and eggs to the sauce and bring it just to a simmer.
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30
Season with salt and pepper.
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31
Remove the pan from the heat and whisk in the remaining 4 tablespoons of butter, 1 tablespoon at a time, occasionally moving the pan back to the burner to keep the sauce very warm.
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32
Stir in the chives.
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33
Pour the sauce over the pappardelle and toss to coat.
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34
Transfer to shallow bowls and serve.
