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["Heat butter and oil in a large pot over medium-high heat. Add onion and garlic and cook, stirring often, until softened and beginning to brown, about 5 minutes. Add corn; season with salt and pepper. Cook, stirring occasionally, until corn is softened and beginning to brown, 6-8 minutes.", "Add thyme sprigs and 5 cups water to pot. Bring corn mixture to a boil, reduce heat, and simmer until corn is very soft, 6-8 minutes longer; discard thyme sprigs.", "Working in batches, puree corn mixture in a blender until smooth (or use an immersion blender in the pot). Strain through a fine-mesh sieve into a large bowl, pressing on solids; discard solids. Transfer soup to a large bowl, cover, and chill until cold, at least 2 hours.", "Pour water into a large pot to a depth of 1""; bring to a boil and salt generously. Add lobsters, cover, and cook until bright red, 8-10 minutes. Transfer lobsters to a rimmed baking sheet and let cool.", "Crack lobster shells, pick meat from tail and claws, and cut into bite-size pieces (you should have about 2 cups meat).", "Whisk shallot, lemon juice, and mustard in a medium bowl. Gradually whisk in 2 tablespoons oil; season dressing with kosher salt and pepper. Add lobster meat, 3 tablespoons celery leaves, and 1 tablespoon tarragon; toss gently to coat. Cover and chill until cold, about 1 hour.", "Divide soup among bowls and top with lobster salad and tarragon and celery leaves. Drizzle with oil and season with sea salt and pepper.", "DO AHEAD:"]
