A highly rated recipe for gourmet chicken a la king is featured on Food network.com. This version requires poaching chicken breast halves and using their meat for the dish.
To poach the chicken, place 3 pounds of chicken breast halves into a saucepan along with 10 sprigs fresh parsley, 2 sprigs fresh thyme and 1/2 each of 1 small onion, 1 small carrot and 1 celery stalk. Pour in 5 to 6 cups chicken broth, and bring to a boil. Reduce heat to very low, cover, and cook for 20 minutes. Remove pan from heat, and take the lid off. Let chicken cool for 30 minutes before transferring to a cutting board, boning, removing its skin and cutting it into cubes.
Melt 1/4 cup unsalted butter in a large saucepan, and cook 2 large minced shallots in butter for four to five minutes. Sprinkle 6 tablespoons of all-purpose flour into the pan, cooking and stirring another two minutes with a wooden spoon. Whisk in 1/4 cup sherry and 3 3/4 cups chicken broth, and bring it to a boil. Add 6 sprigs plus 1 tablespoon fresh flat-leaf parsley and 1 sprig fresh thyme. Lower the heat and simmer, stirring frequently, for 30 minutes.
In a large skillet, cook 1/2 pound trimmed and sliced shiitake mushrooms in 1 tablespoon unsalted butter, and cook for 5 minutes. Season mushrooms with salt and pepper, and strain sauce mixture into the mushrooms. Add 1 teaspoon kosher salt, 1/2 teaspoon black pepper, a pinch of cayenne pepper and a pinch of freshly grated nutmeg. Whisk in 1/2 cup creme fraiche or heavy cream. Stir in the minced parsley, 1 tablespoon snipped fresh chives and 4 cups cubed chicken.
Simmer, and add more salt and pepper to taste.