Spray a 2 quart casserole dish with cooking spray. Place the frozen broccoli in the bottom of the dish then drain and add mushrooms on top of broccoli. Brown the chicken pieces and onion in 2 tablespoons of the butter in a skillet on top of the stove, remove from skillet and layer over the mushrooms.
Add the other 2 tablespoons butter to your skillet where you browned the chicken along with the flour and make a roux like you are making gravy. Combine chicken broth, milk, black pepper, salt, nutmeg, and tumeric and pour into skillet.
Bring to slow boil and cook until thick like cream gravy. Pour over chicken in casserole dish and sprinkle on shredded cheese. Bake in 350 preheated oven for 40 to 45 minutes. Makes 6 to 8 servings.