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Peel the shrimp, reserving the shells and tails. Devein the shrimp and chill in the fridge. In a large nonreactive pot over medium-high heat, sear the shrimp shells and tails with 2 tablespoons olive oil, stirring until bright red, about 3 minutes. Add 1 cup wine, simmer for 10 minutes, then add 3 1⁄2 cups water, bring to a boil, reduce heat to low, and simmer for 45 minutes or until the liquid reduces to about 1 1⁄2 cups. Strain and reserve.
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In a cold, nonreactive pot, add 1⁄2 cup olive oil and the chopped garlic. Over medium heat, saute the garlic slowly, stirring constantly, until golden, about 4 minutes. Add the fennel and onion and stir, scraping the garlic off the bottom of the pot so it doesn’t burn and cook, about 5 minutes. Add remaining cup of white wine and cook until it evaporates, about 15 minutes. Add 4 cups of water and 1 tablespoon salt.
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Bring to a boil, then reduce to a simmer and cook for 30 minutes, or until the liquid has reduced to about 21⁄2 cups. Remove pan from heat and cool for 15 minutes. Stir in the reserved shrimp stock. Transfer to a blender in batches and blend until smooth. If needed, you can thin with water or thicken by simmering down the liquid, stirring occasionally, over medium heat.
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Warm a large skillet with 2 tablespoons olive oil. Add the green garlic and 1 teaspoon of water. Sweat lightly, ensuring the greens don’t begin to brown. Add the shrimp in a single layer. Season with 1 teaspoon salt. Gently cook the shrimp on each side until just pink, about 4 minutes total. Add the lemon juice and remove the pan from the heat.
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Reheat the soup if necessary. In 6 individual soup bowls place a dollop of yogurt and three pieces of shrimp. Sprinkle in some pepper flakes and a small fennel frond, carefully ladle in soup, and serve.