Rinse and slice the mushrooms and set aside.
In a 3-quart sauce pan, heat 2 tablespoons of oil and add the onions, garlic, potatoes and green beans. Saute over moderate heat, stirring continuously until the onions are transparent.
Add the remaining tablespoon of oil and mushrooms and toss. Cover the pan and cook 2 minutes over low heat. Add the chicken broth, tomatoes and herbs to the pan and stir.
Raise the heat to high and bring the soup to a boil, then reduce the heat and slowly simmer for 45 minutes.
Slowly add 1/2 cup of the hot soup to the beaten egg yolk, stirring and blending well. Add this mixture to the soup in the pan and mix well. ladle into individual soup bowls and sprinkle with the grated cheese. Serve.