Fill a large pot with 6 to 8 quarts salted water and set over medium heat. While waiting for the water to boil, make the sauce.
Using a sharp knife, trim the fat from the edges of the prosciutto slices. Chop and reserve the fat. Cut the prosciutto into bite-size pieces and set aside.
In a large, heavy skillet over medium high heat, melt 2 tablespoons of the butter until foamy. Add the reserved chopped fat and the onions and cook, stirring frequently, until the onions are golden brown, 8 to 10 minutes. Stir in half of the reserved prosciutto and cook for 1 minute. Add the tomatoes and cook for 3 minutes, or until the sauce is thickened. Add the peas and remove from the heat.
Increase the heat to high under the salted water and bring to a boil. Add the pasta rags and cook until tender but still "al dente," about 1 minute. (This will depend upon the thickness of the fresh pasta.) Drain in a colander.
Return the pasta sauce to the heat and, when bubbling, add the remaining 3 tablespoons of butter, the cooked pasta, and the remaining prosciutto. Toss thoroughly to combine. Season, to taste, with freshly ground black pepper and serve immediately, passing the cheese with the pasta.
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