The chicken in these cutlets is tender and moist, and its gentle flavor is not challenged by the mild cheese. The mushroom white sauce is just right. Skewering the cutlets together is tricky; it may take a little practice.
Bone and skin the chicken breasts. Cut each whole breast in half and cut each half into 2 cutlets. Pound each cutlet to about 1/8-inch thick. Mix salt with 3 tablespoons flour and coat chicken with this mixture. In a skillet, melt 3 tablespoons butter, add cutlets a few at a time, and sauté until lightly browned on both sides, adding more butter if necessary. Remove cutlets from the skillet. Arrange cheese slices on 6 cutlets; top with remaining cutlets and skewer layers together with toothpicks. Set aside. In the drippings, melt the remaining 2 tablespoons butter. Add mushrooms and cook until tender, stirring occasionally. Stir in pepper and the remaining 1 tablespoon flour; blend well. Gradually stir in water, milk, wine, and bouillon. Heat to boiling, stirring to loosen brown bits from the bottom of the skillet. Return cutlets to skillet; heat to boiling. Reduce heat to low; cover and simmer for 5 minutes or until cheese is melted. Carefully remove toothpicks. Spoon cutlets and sauce onto a large platter; garnish with parsley sprigs.