Preheat oven to 350°F. Boil chicken for about 45 minutes. Set aside. Cook broccoli for about 10 minutes.
Spray 13x9 pan with cooking spray. First put broccoli on bottom of pan. Cut or tear chicken into bite size pieces and put on top of broccoli. Mix together both soups and the Miracle Whip or Mayo and put on top of chicken layer. Top with shredded cheese using as much as you like.