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1
Remove the claws from the lobsters.
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2
Carefully crack the claws, and remove the meat in one piece if you can.
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3
Remove the tail meat and chop it into 1-inch chunks.
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4
Set the lobster aside in the refrigerator.
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5
Coarsely chop the shells and reserve.
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6
Melt the butter in a large pot over medium-high heat.
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7
Add the onion and cook until soft, about 4 minutes.
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8
Add the garlic and cook for 30 seconds.
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9
Raise the heat to high, add the wine, lobster shells, and corncobs, and cook until the wine has completely reduced.
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10
Add the 4 cups lobster stock and bring to a boil.
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11
Reduce the heat and simmer for 15 minutes.
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12
Strain the broth into a bowl, discard the shells and corncobs, and return the broth to the pot.
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13
Add 1 cup of the roasted corn kernels and cook until the corn is just tender, 15 minutes.
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14
Transfer the soup to a blender, in batches, and puree until smooth.
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15
Strain into a clean saucepan and bring to a simmer.
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16
Stir in the remaining 1 cup roasted corn kernels, and the chiles, and cook for 5 minutes.
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17
Meanwhile, put the heavy cream in a medium saucepan, bring it to a simmer over medium heat, and cook until reduced by half, about 10 minutes.
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18
Add the reduced cream to the chowder and simmer for 5 minutes.
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19
If the chowder appears too thick, add additional stock or water to thin it slightly.
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20
Add the reserved chopped lobster meat, season with salt and pepper, and stir in the chopped cilantro.
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21
Ladle the chowder into bowls and top each one with a few tablespoons of the relish, a lobster claw, and a few fresh cilantro leaves.
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22
Combine the corn, poblano, onion, lime juice, honey, and oil in a medium bowl and season with salt and pepper.
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23
Let the relish sit at room temperature for at least 30 minutes to allow the flavors to meld.
