Soften mushrooms in warm water for 20 minutes.
Place the Fontina cheese in a bowl, cover with the milk and soak for several hours in the refrigerator.
Melt half the butter in a saucepan and saute the onion over low heat until transparent. Add the mushrooms and cook until soft. Next add the rice and stir until the rice absorbs the butter. Pour in the wine and stir. When the wine has been absorbed, add the beef broth a little at a time, stirring continuously until fully absorbed. Cook for 10 minutes longer. Turn off the heat, cover the saucepan and let stand for a few more minutes without stirring until the rice is soft but al dente.
While the rice is cooking, prepare the sauce.
Put the softened cheese and milk into a double boiler and cook over medium heat until the cheese starts to melt. Then stir in the egg yolks and the rest of the butter. Keep stirring until the cheese has completely melted and the mixture is uniformly blended. Sprinkle with salt.
Put the rice into a warmed serving bowl, pour the cheese mixture over it and serve immediately.