This recipe gets the most out of shrimp by first turning the shells into a fragrant and flavorful stock, then transforming the stock into an elegant garlic cream sauce for pasta. The shelled shrimp are then gently cooked in the sauce, making this dish a shrimp lover's dream.
For the shrimp stock: Peel and devein the shrimp, reserving the shells. Put the shrimp in a bowl over ice, cover and refrigerate.
Heat the oil in a large saucepan over medium-high heat. Add the celery, garlic and onion and cook until softened, about 7 minutes. Stir in the shrimp shells and cook until light pink, 1 minute. Stir in the tomato paste. Add the white wine and bring to a simmer. Simmer until only a few tablespoons remain in the pan, about 3 minutes. Add the peppercorns, bay leaves, thyme, parsley and 3 cups cold water. Bring to a boil over high heat. Reduce to a simmer and simmer over medium-low heat until reduced by half, about 15 minutes. Stir in 1 teaspoon salt.
Strain the stock, pressing on the solids to extract any liquid. You should have about 2 cups. Set aside.
For the pasta: Bring a large pot of salted water to a boil. Add the pasta and cook according to the package instructions for al dente. Drain and set aside.
Melt the butter in a large skillet over medium heat. Stir in the paprika and garlic and cook, stirring, until the butter is fragrant and vibrant red, about 30 seconds. Add the shrimp stock and bring to a boil over high heat. Cook until reduced by half, about 5 minutes.
Stir in the cream and reduce to a simmer. Simmer over medium-low heat, stirring occasionally, until slightly thickened, 2 to 3 minutes. Add the shrimp and cook until firm and cooked through, 4 to 5 minutes. Add the pasta and Parmesan and toss until well coated (see Cook's Note). Season with salt and sprinkle with parsley.
Don't worry if it seems like there is too much sauce. As soon as everything is tossed together, the sauce will start to cling to the pasta and thicken before your eyes.
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