Heat the oven to 375°F and arrange the chicken cutlets down the center of a 9-by-13-inch baking dish.
Season the chicken with the salt and black pepper and arrange the green beans along both sides.
Sprinkle the stuffing mix loosely over and around the chicken, then pour the broth slowly across all of the dry crumbs.
Spoon the cranberry sauce in small patches over the moistened stuffing and chicken.
Cover tightly with foil and bake for 30 minutes.
Uncover and bake for 15 to 20 minutes more, until the stuffing browns and the thickest chicken piece reaches 165°F.