Bring 6 quarts water to a rolling boil and add 2 tablespoons salt.
Heat the olive oil over a medium flame until hot but not smoking. Add the garlic, chicken livers, peas, salt, to taste, and cook until the meat is browned and the peas are soft, about 7 minutes.
While the meat browns, add the perciatelli to the boiling water and cook, according to the package directions, until tender but still al dente.
Meanwhile, reheat the Ragu alla Napoletana in a separate saucepan. Drain the cooked pasta and add to the saucepan with the ragu. Add the chicken livers and peas and toss over high heat until the ingredients are well combined. Add the chili flakes and the mozzarella and toss again, so the mozzarella melts amidst the noodles. Serve immediately in 4 warmed pasta bowls. Garnish, to taste, with the Parmigiano.
Ragu: In a 12 to 14-inch saucepan, heat the oil over a medium-high flame until hot but not smoking. Add the onion and garlic and cook until soft and light golden brown, about 5 minutes. Add the meat and the prosciutto, and continue cooking until the meat has browned, about 5 minutes more. Add the red wine. Cook over medium heat until the wine has been absorbed into the meat. Season, to taste, with salt and pepper. Add the tomato paste, the pureed tomatoes, and enough water to just cover the meat. Stir to combine and let the mixture boil for 2 hours, adding more water, if necessary, to keep the pan moist.
When finished simmering, the sauce will be extremely thick, more like a meat mixture than a sauce.