Preheat oven to 350°F. Cook rice in chicken broth with olive oil until tender, then add broccoli and cook until done.
Cook chicken in butter until golden, then combine with cooked rice, broccoli, cream of chicken soup, milk, sour cream, seasonings, and half of the cheese.
Transfer mixture to a greased casserole dish, top with remaining cheese, and bake covered for 15 minutes. Then, sprinkle crushed crackers mixed with melted butter on top and bake uncovered for 10 minutes.
Notes
For a quicker version, use rotisserie chicken and pre-cooked rice.