In a skillet, sauté the pancetta for a few minutes, then set aside. Meanwhile, slice the mushrooms and sauté them in a little oil for a few minutes.
In a large pot or saucepan, pour in the water, then the oil.
Add the pasta, the previously peeled and sliced onion, the pancetta, the eggs, the mushrooms, as well as the cheese. Season with salt and pepper, then cover until boiling.
To finish, when the water boils, remove the lid and let it cook for about 15 minutes, stirring occasionally, until the water is absorbed. Adjust the seasoning, and divide the pasta onto a plate. Sprinkle with cheese to taste and chives before enjoying.