1. Bring a large pot of salted water to a boil. Add peas and cook until bright green and tender, about 7 to 8 minutes. Remove the peas with a slotted spoon or strainer and set aside. Use the same water to cook pasta according to package directions. Drain, reserving 1/4 cup of the pasta water.
2. Meanwhile, in a large skillet heat butter over medium heat. Add the prosciutto or pancetta and cook until golden and crispy, about 5 to 6 minutes. Add the shallot and thyme and cook until slightly softened, but not brown, about 1 minute. Increase the heat to medium-high and add the wine. Let the wine evaporate slightly and then add the heavy cream. Cook until the sauce reduces and thickens slightly, stirring occasionally, about 6 to 7 minutes. Season with salt and pepper. Just before serving, stir the cheese, parsley, and peas into the sauce until it thickens a little more.
3. Toss the pasta in the sauce and use the reserved pasta water, if needed, to loosen the sauce slightly. Transfer the pasta to serving bowls and garnish with additional cheese and parsley, if desired.