Bring the water and 4 tablespoons of butter to a boil in a medium sauce pan over medium-high heat. Add the stuffing mix and stir well. Remove from heat and allow to sit for 5 minutes before fluffing with a fork.

Preheat oven to 400 degrees.

Cut each chicken breast in half lengthwise to make 6 thin chicken breasts. Season each chicken breast on both sides with ground black pepper (the amount you use is up to you).

Melt 1 tablespoon of butter in a large skillet over medium heat. Add the chicken breasts and cook on each side for about 5 minutes, until the internal temperature of each chicken breast reaches 165 degrees. Remove the chicken breasts from the pan and set aside. Do not discard the butter and chicken juices in the pan.

Add the green beans, mushrooms, and onion to the pan; Cover and cook over medium heat for 8 minutes, or until the vegetables are beginning to become tender.

Add ¼ cup flour to the vegetables and stir well (the flour will stick to the vegetables, which is fine). Cook over medium heat for 1 minute, stirring constantly to prevent the flour from burning.

Add the chicken broth and stir well. Cook for 3 minutes over medium heat until the sauce is thickened. Add the cream cheese and stir until melted and combined into the sauce.

Grease a 9x13 inch glass baking dish. Add the cooked chicken breasts to the baking dish then pour the creamy vegetable sauce over the chicken. Spoon the prepared stuffing evenly over the top of the casserole.

Bake the casserole at 400 degrees for 30 minutes.