In a large, deep saucepan, heat 1 tablespoon butter over medium-high heat. Add the fingerling potatoes, garlic, chiles, shallots, and corn and stir. Season with a big pinch of salt, and let that sweat, about 2 to 3 minutes.
Strain about 2 cups corn lobster stock directly into the potato corn mixture. Stir, taste and season with salt and freshly cracked black pepper. Slowly add the cream, then stir in the remaining 2 tablespoons of butter. Gently mix to combine. Reduce the heat to make sure the butter and cream do not separate. Add the lobster chunks, basting with the butter mixture until warmed through, about 2 to 3 only. Taste and season with salt and black pepper, to taste. Transfer the chowder to serving bowls and garnish with tarragon and lime zest.
Put wine, water, bay leaves, black peppercorns, lemon and onion into a large stockpot and bring to a boil. Put the lobsters into a deep container and pour the court bouillon over the lobsters. Let the lobsters sit for about 3 1/2 minutes before carefully removing the tails and plunging them into an ice bath. Let the claws continue to steep for another 2 minutes. Remove the claws from the court bouillon and put them into the ice bath. Reserve the court bouillon. Once cool enough to handle, remove the lobster meat from the shells and set aside for the chowder. Reserve the shells separately.
To a large, deep pot over medium heat, add the blended olive oil and heat until smoking hot. Add the shells to the pot and stir to coat, allowing them to sweat. Break the ears of corn in half and add to the pot, along with the chile, and the bay leaf. Pour in the reserved court bouillon liquid and season with salt, to taste. Bring to a simmer and let cook for about 20 to 30 minutes. Remove the kernels from the corn and set aside for the chowder.
Yield: about 4 cups