Preheat the oven to 400˚F.
In a large bowl, mix cream of chicken soup, cheese soup, shredded chicken breast, broccoli florets, (uncooked) rice, chicken broth and sour cream together until everything is incorporated, then spread the mixture into a 9x13 baking dish.
Sprinkle the shredded cheddar cheese evenly over the top. Cover with foil.
Bake on the middle rack of the oven for 40 minutes. Remove the foil and bake for an additional 10 minutes. Optional: Broil for the last 3-4 minutes to create crispy bits on the top. Enjoy!
