Dry the chicken thoroughly with paper towels. In a large, heavy skillet heat 3 tablespoons of the butter over moderate heat. Add the chicken, skin side down, and saute, turning to brown evenly on all sides. Remove to a plate and set aside.
Add the scallions and mushrooms to the skillet and cook until the vegetables are lightly browned, stirring frequently. Return the chicken to the skillet. Add the broth, sherry, and salt and pepper. Cover and simmer until tender.
Transfer the chicken and vegetables to a serving platter and keep warm. Reserve the cooking liquid in the skillet.
In a small saucepan melt the remaining 2 tablespoons butter over low heat. Add the flour and cook 3 or 4 minutes, stirring constantly. Gradually add the cream and the reserved cooking liquid from the chicken, stirring constantly with a wire whisk. Simmer until the sauce is smooth, thickened, and hot. Stir in the tarragon and walnuts, taste for seasoning, and pour over the chicken. Serve with buttered noodles and buttered green peas or asparagus tips.
Submitted by: CM
