In a large pot of boiling salted water, cook the pasta until al dente. Drain, reserving 3 tablespoons of the cooking water.
Meanwhile, in a large skillet, heat the oil. Add the pancetta and cook over moderate heat until most of the fat has been rendered, 7 minutes. Add the shallot and garlic and cook over moderate heat for 1 minute. Add the cream and simmer over moderate heat until slightly thickened, about 2 minutes. Add the hot pasta to the skillet and stir to coat, 1 minute. Remove from the heat. Stir in the reserved pasta cooking water, the 2 tablespoons of grated cheese and the egg yolks. Season with salt. Divide the pasta into bowls and sprinkle with parsley and pepper. Serve, passing more cheese at the table.