Bring a large pot of water to a boil, salt it and add the pasta. Cook to al dente; drain, reserving 1/2 cup of the pasta cooking water. While the pasta is working, lightly toast the pine nuts for the pesto.
Combine the pesto ingredients, including the toasted nuts, in a food processor and pulse into a paste.
Melt the butter in a large skillet over medium heat, add the shallot and stir for a couple of minutes. Add the prosciutto and stir for a minute more, then add the peas and stir to heat through. Stir in the wine (or stock) and cook to reduce, 2 to 3 minutes. Stir in the cream and season the sauce with salt and pepper. Lower the heat; let bubble and thicken for a few minutes.
Toss the pasta with the cream sauce and the pesto, using a splash of the reserved cooking water to loosen if desired. Pass extra cheese at the table.