Bring a large pot of water to a rolling boil. Salt generously and cook the spaghetti according to the package directions until al dente. Retrieve the pasta and drain in a colander, reserving the salted water in the pot. Drop the peas into the pasta water and cook just a few moments until bright green and still with some bite. Reserve 1 1/2 cups of the pasta water and drain the peas.
As the pasta is finishing its cooking, melt the butter in a deep sided sauté pan over medium low heat. Stir in the mascarpone and crème fraîche and season to taste with salt and pepper. Once the sauce is creamy, add the spaghetti and peas and toss to coat. If adding shredded chicken, add it as well. Add the pasta water, 1/2 cup at a time, adding in increments until the desired consistency is reached. Stir in the Parmesan cheese.