Add enough water to the mushrooms to cover them and set aside.
In a small skillet, cook the pancetta or bacon over moderately low heat, stirring occasionally, until the fat is rendered and the meat is tender, about 15 minutes.
Let cool slightly and add the mushrooms.
While the pancetta or bacon is cooking, bring a large pan of water to boil. Add salt when the water begins to boil, add pasta and cook until al dente.
Drain, hold back 1 cup of the cooking water.
In a large bowl, whisk the egg yolks and egg with the pancetta or bacon and the rendered fat.
Add the pasta, 1/4 cup of the water that you set aside and 2/3 cup of the cheese mixture to the egg mixture and toss until creamy, about 1 minute; add more of the cooking water if necessary.
Add crushed peppers and season with salt and pepper.
Serve in shallow bowls, sprinkle with remaining cheese and top with chopped parsley.