Soak the ceps in warm water for 20 minutes. Drain them, retaining the strained soaking water. Squeeze the ceps dry and finely chop them.
Heat the oil and gently fry the button mushrooms. Add the ceps with 2-3 tbsp soaking water and cook for about 5 minutes. Remove from the heat and gently stir in the ricotta, Fontina and Pecorino cheeses, and the beaten eggs. (The eggs should not be cooked so that they remain liquid at this stage). Taste and add salt if necessary and pepper.
Meanwhile cook the pasta for 6-7 minutes or until al dente, and drain. Return the pasta to the empty pan, and mix well with the sauce, so that the egg just starts to thicken with the heat of the pasta.