- Bring 4 quarts water to boil in large pot. Add spaghetti and 1 tablespoon salt and cook, stirring often, until al dente. Reserve 1/4 cup cooking water, then drain spaghetti and return it to pot.
- Meanwhile, pat shrimp dry with paper towels and season with salt and pepper. Heat 1 tablespoon oil in 12-inch nonstick skillet over medium-high heat until just smoking. Add half of shrimp to pan in single layer and cook until spotty brown and cooked through, about 2 minutes per side. Transfer shrimp to plate and tent loosely with aluminum foil. Repeat with 1 tablespoon oil and remaining shrimp.
- Return now-empty skillet to medium-high heat, add remaining 1 tablespoon oil and shallot, and cook until shallot is softened, about 2 minutes. Add garlic and cook until fragrant, about 30 seconds. Add wine, bring to boil, and cook until reduced by half, about 2 minutes. Stir in cream and reserved cooking water and bring to boil again. Off heat, stir in tarragon, lemon juice, 1/4 teaspoon salt, 1/4 teaspoon pepper, and shrimp. Add sauce to spaghetti and toss to coat. Serve.
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