The Food Network offers a recipe for Chicken a la King. To make this recipe, sauté two minced large shallots in 1/4 cup unsalted butter until softened.
Sprinkle in 6 tablespoons all-purpose flour; cook and stir for 2 minutes. Whisk in 1/4 cup dry sherry and 3 3/4 cups chicken broth, bringing to a boil while stirring. Add six sprigs parsley and one sprig thyme; lower the heat and simmer. Cook for 30 minutes, stirring often.
Meanwhile, sauté 1/2 pound sliced shiitake mushrooms in 1 tablespoon unsalted butter until golden brown. Add salt and freshly ground black pepper to taste. Strain the sauce into the mushrooms and season with salt and pepper to taste. Add a pinch of cayenne pepper and a pinch of grated nutmeg; whisk in 1/2 cup crème fraiche or heavy cream.
Meanwhile, poach 3 pounds chicken breast halves. To poach the chicken, add 10 sprigs parsley, two sprigs thyme, one small halved onion, one small halved carrot, one small halved stalk celery and chicken to a medium saucepan. Cover with 5 to 6 cups chicken broth and bring just to a boil. Turn the heat to very low and poach, covered, for 20 minutes or until firm to the touch. Remove from heat, uncover, and cool the chicken in the liquid for 30 minutes.
Cut the chicken into 1-inch cubes. Add 1 tablespoon minced parsley, 4 cups poached chicken and 1 tablespoon snipped fresh chives to the sauce; bring to a simmer. Season with salt and pepper to taste. Serve promptly over noodles, biscuits, toast points or wrapped in crepes.