1. Place the chicken pieces in a stove-top covered casserole and add the 2 cups of water. Bring to a boil. Soak the mushrooms and drain them through a fine strainer, reserving the soaking water.
2. Chop the mushrooms. Add the celery, carrot, parsley, mushrooms, along with the strained soaking water. Add a bit of salt and pepper to taste and simmer the whole, covered, for about 1 hour.
3. Remove the chicken to a heated platter and thicken the pan liquid with the roux. Add the wine and bring the sauce to a simmer. Remove the pan from the heat.
4. Place the egg yolks in a 2-cup glassmeasuring cup and add about ˝ cup of the sauce, stirring all the time. Blend this mixture into the sauce in the pot, then return the chicken to the pot.
5. Test for salt and pepper. Heat the dish to serving temperature but not to a simmer or the eggs will curdle.
