Remove the claws from the lobsters. Carefully crack the claws and try to remove the meat in 1 piece and set aside for garnish. Remove the tail meat and chop into 1-inch chunks and set aside in the refrigerator. Reserve the shells.
Melt butter in a medium stockpot over medium heat; add the onions and garlic and cook until soft. Increase heat to high, add the wine, lobster shells, and corn cobs and cook until completely reduced. Add 4 cups of the lobster stock and bring to a boil. Add 2 cups of the corn and let cook for 15 minutes. Remove the lobster shells and corn cobs.
Transfer the soup to a food processor and process until smooth. Strain into a clean saucepan and bring to a simmer. Stir in the lobster meat, remaining 1 cup of roasted corn kernels and green chiles and cook for 5 minutes.
Place heavy cream in a medium saucepan and reduce by half. Add the reduced cream to the chowder and stir until combined, if the chowder appears too thick, add some of the remaining lobster stock to thinly slightly. Season with salt and pepper and stir in the cilantro. Ladle into bowls and top with a few tablespoons of relish, a lobster claw and fresh cilantro leaves.
Preheat oven to 425 degrees F.
Remove corn from water, place on baking sheets and roast in the oven until tender and slightly charred, 15 to 20 minutes. Let cool slightly, remove husks and kernels and place kernels in a bowl.
Add the remaining ingredients and stir until combined. Let relish sit at room temperature for at least 15 minutes to allow flavors to meld.
To roast corn: Remove the silks from the corn, but leave the husks on. Soak in cold water for 10 minutes. Preheat oven to 425 degrees F. Remove corn from water, place on baking sheets and roast in the oven until tender and slightly charred, 15 to 20 minutes. Let cool slightly, remove husks and kernels and place kernels in a bowl. You can also do this on a grill.
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