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1
Bring a large pot of salted water to a boil.
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2
Add the lobsters and cook until they are bright red, about 7 minutes.
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3
Reserve 2 tablespoons of the lobster cooking water, then drain the lobsters.
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4
Transfer the lobsters to a large rimmed baking sheet and let them cool slightly.
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5
Twist the lobster tails from the bodies.
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6
With scissors, cut down the length of each tail shell and remove the meat.
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7
Cut the tails in half lengthwise and discard the dark intestine.
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8
Crack the claws and remove the meat.
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9
Cover the lobster and refrigerate.
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10
Meanwhile, in a large bowl, mix the cold water with 1 tablespoon of the lemon juice.
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11
Add the fennel and refrigerate for about 25 minutes, until the fennel is very crisp.
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12
In a medium bowl, mix the mayonnaise with the tarragon, the reserved lobster cooking liquid and the remaining 2 tablespoons of lemon juice.
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13
Season the dressing with salt and pepper.
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14
Drain the fennel and pat dry with paper towels; transfer to a large bowl.
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15
Add the arugula, shallot and cilantro leaves and toss well.
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16
Add all but 1/4 cup of the dressing to the bowl and toss well.
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17
Arrange the salad on plates and top each one with a claw and half a lobster tail.
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18
Drizzle the lobster with the remaining dressing and serve at once.
