Heat plenty of water in a large saucepan, add a teaspoon of salt and, when it starts to boil, add the pasta. Cook over high heat for a couple of minutes less those indicated on the package.
The pasta has to be slightly hard so that it doesn’t go too far when we give it a final blow of cooking in the sauce. When it is at this point we drain it and reserve part of the cooking water, we will use it to form the sauce. We keep the water very hot.
Clean the mushrooms with a wet rag, removing well the remains of earth that they may contain. We cut them into 1/2 cm slices and then into sticks or lardons. Heat the butter and oil in a large frying pan and fry until no liquid remains.
Peel and grate the garlic cloves and add them to the pan with the mushrooms. Stir and fry for a few more minutes or until dry and slightly crispy. Meanwhile, beat the egg yolks with the grated cheese and a little ground black pepper.
Heat the pasta in the pan together with the egg and cheese mixture, adding a saucepan of the water used to cook the pasta, very hot. We mix for bind the sauce and cook for a couple of minutes. If we want a lighter sauce, we add more water. We serve immediately decorating the plate with parsley leaves and grating a little cheese on the surface.