Chop a 4-pound chicken into 11 pieces, and season the pieces with salt and pepper. Brown the chicken on both sides in 2 tablespoons of butter over medium-high heat. Lower the heat slightly, and add 1 cup of diced onion, 1/2 cup of diced carrot and 1/3 cup of diced celery. Cook the vegetables until they are tender.
Stir in 8 ounces of quartered mushrooms. When the mushrooms release their juices, whisk in 2 tablespoons of flour. Pour in 2/3 cup of dry white wine, and allow it to boil for just under a minute before stirring in 4 cups of chicken broth. Distribute the chicken pieces, skin-side up, on top of the vegetables. Tie 2 sprigs each of flat-leaf parsley and thyme with one bay leaf, and immerse the bouquet in the liquid.
Simmer the mixture, partially covered, for about 25 minutes or until the chicken is done. Remove the chicken from the pot. Simmer the mixture, uncovered, for another five minutes, and remove the herbs. Beat 2 egg yolks with 1/4 cup of cream, and gradually whisk in 1/2 cup of cooking liquid before stirring the mixture into the pot. Put the chicken back into the pot, and incorporate 1 tablespoon of butter, and 2 tablespoons each of chopped tarragon and lemon juice. Simmer the mixture briefly, stir, and serve the dish.Learn more about Cooking