My mom always made this for us with or without chicken and we would all gobble it up. She would use this huge metal baking pan that had to be at least 40 years old and had just about everything cooked in it. This is one of the dishes made in it.
In a saucepan, bring 1 cup water and a dash of salt to a boil, then add rice, stir, and turn heat to medium-low and cover.
Cut your chicken into cubes and cook it in a fry pan with a olive oil until done, then season with a little salt & pepper; set aside. At this point, your rice should be done, uncover and fluff with a fork, then turn the heat off and cover; set aside. In a deep sauce pan, add your soups, and milk. Once it starts to get hot, add your American cheese, and half of your sharp cheese. Once the cheese is melted, add the cubed chicken and onion, and combine everything thoroughly. Pour soup mixture over rice the stir everything until evenly incorporated; set aside. In a microwave safe bowl, steam your broccoli in the microwave using the directions on the back of your package. Add broccoli to rice mixture and mix well. Spread your mixture in a casserole dish and flatten out then cover with the remaining cheddar cheese and bake in a pre-heated 425 degree oven for 20 minutes.