Arrange chicken in a 13- x 9-inch baking dish coated with cooking spray. Top chicken with ham and cheese.
Coat a nonstick skillet with cooking spray; place over medium-high heat until hot. Add mushrooms; sauté 5 minutes or until tender. Combine mushrooms, soup, and broth. Spoon mixture over chicken. Top with stuffing mix; coat well with cooking spray. Bake at 350° for 45 minutes.
Tip: This dish is a casserole version of classic chicken cordon bleu in which a thin piece of chicken is topped with a slice of prosciutto, a slice of Swiss cheese, and another slice of chicken. The stacked chicken is then breaded and sautéed until golden.