Cut the chicken into 8 pieces. Rinse it under cold water and pat dry. Season with garlic salt and pepper. Heat the butter in a skillet and when it foams, quickly sauté the chicken pieces, turning them so that they cook on both sides but do not brown. This seizes the skin so it does not shrivel during cooking. Drain the chicken on paper towels.
Put the hominy in a 2-quart casserole with a lid. Lay the chicken pieces on top and cover with an even layer of onion, sliced mushrooms, and carrot. Add the bay leaf and sprinkle the pepper and dried thyme over the vegetables. Add the wine and cover the casserole.
Cook in a preheated 325°F degree oven for 45 minutes. About 5 minutes before the casserole is finished cooking, add the salt and parsley. Take it from the oven and remove the bay leaf. Taste and add the cream if you want it.