Fill a large pot with water, add 1 tablespoon of salt, and bring to a boil.
Meanwhile, melt 2 tablespoons of the butter in a large (12-inch) saute pan over medium heat. Add the prosciutto and cook for 5 minutes, separating the slices with tongs, until crisp. Remove to a plate and set aside. Add the remaining tablespoon of butter and the onion to the saute pan and cook for 5 minutes, stirring occasionally, until tender. Add the garlic and cook for 1 more minute. Add the cream, Gorgonzola, 1 1/2 teaspoons salt, and the pepper and bring the sauce to a boil. Lower the heat and simmer for 5 minutes, until thickened. Turn off the heat.
When the sauce is almost done, add the pasta to the pot of boiling water and cook according to the package directions. Reserve 1 cup of the pasta water and drain the pasta, allowing some of the water to remain. Pour the pasta into the pan with the sauce. Add the peas, Parmesan, basil, and prosciutto and toss well. If the pasta seems dry, add some of the reserved pasta water. Taste for seasonings and serve hot with extra Parmesan.