Slice 5 ounces prosciutto crosswise into 1/4-inch-wide strips; set aside. Mince remaining 1 ounce prosciutto. Melt butter in 10-inch skillet over medium-low heat. Add shallot and 1/4 teaspoon salt and cook until softened, about 2 minutes. Stir in cream and minced prosciutto and bring to simmer. Cook, stirring occasionally, until cream mixture measures 1 cup, 5 to 7 minutes. Remove pan from heat and cover to keep warm.
2.
Meanwhile, bring 4 quarts water to boil in large pot. Add pasta and 1 tablespoon salt and cook, stirring often, until al dente. Reserve 2 cups cooking water, then drain pasta and return it to pot.
3.
Add 1 cup reserved cooking water, cream mixture, prosciutto strips, peas, Parmesan, Gruyère, and 1 teaspoon pepper to pasta. Gently toss until pasta is well coated. Transfer pasta to serving bowl and serve immediately, adjusting consistency with remaining reserved cooking water as needed.
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