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1
Set a large 2 to 3 gallon stockpot to boil over high heat.
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2
Once the water comes to a boil, immerse the lobsters in the pot.
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3
Cook the lobsters for 3 minutes, remove, and chill immediately in an ice bath.
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4
Once the lobsters are cool enough to handle, remove from the water and place on a kitchen towel draped over a cutting board.
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5
Twist the tails off the lobsters, and cut the tails in half lengthwise using a large chef's knife (score along the length of the tail).
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6
Set the cut tails aside, and crack the shells of the claws to remove the meat.
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7
Reserve the claw meat for pasta or a salad for a later date.
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8
Place the Jerusalem artichokes in a 1-quart saucepan, and cover with water.
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9
Set over high heat and bring to a boil.
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10
Once the water comes to a boil, cook the artichokes for 15 minutes, or until easily pierced with a knife.
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11
Remove from the heat, drain, and place the artichokes in a food processor with the heavy cream, 1 tablespoon of butter, 1/4 teaspoon of salt and 1/8 teaspoon of white pepper.
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12
Process the artichokes for 10 to 15 seconds, or until a smooth puree is formed.
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13
Remove from the bowl of the food processor, and place in a heat resistant bowl set over a water bath to keep warm.
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14
Trim the ends off of the asparagus and blanch in boiling water for 2 minutes.
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15
After 2 minutes, remove from the water and cool in ice water.
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16
Once the asparagus is cool enough to handle, remove from the ice water and pat dry with a paper towel.
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17
Cut the asparagus into thirds on a bias.
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18
Set a small saucepan over a low heat and add 4 tablespoons of the remaining butter, the lemon zest, and the lemon juice.
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19
Bring to a gentle simmer and cook for 3 to 4 minutes, allowing the flavors to meld, and season with a pinch of salt, white pepper, and the chopped tarragon.
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20
Set aside, but keep warm.
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21
To finish the dish, set the grill on medium-high.
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22
Brush the lobster tails with the olive oil on the cut end, and season with the remaining 1/4 teaspoon of salt and 1/8 teaspoon of white pepper.
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23
Place the tails, cut-side down, on the grill, and cook for 3 minutes.
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24
Rotate 45 degrees, and cook for an additional 3 minutes.
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25
Turn the lobsters over and cook for 2 minutes.
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26
While the lobsters are cooking on the shell side, place a small skillet over medium-high heat, and once the pan is hot, add the remaining 1 teaspoon of butter and saute the asparagus, tossing, for 1 minute.
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27
Season lightly with salt and white pepper.
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28
To plate the dish, divide the Jerusalem artichoke puree evenly between 2 warmed dinner plates or wide shallow bowls.
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29
Arrange the asparagus around the artichoke puree, and place the lobster tails on top of the puree.
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30
Pour 2 tablespoons of the lemon- tarragon butter over each serving of lobster and garnish with additional tarragon if desired.
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31
Serve immediately.