Preheat the oven to 350° F.
Cut chicken into bite-sized pieces and season with Italian seasoning and desired amount of salt and pepper.
Heat butter in a large pot over medium heat until melted. Add the chicken and cook until golden brown on all sides, about 5 minutes. Remove and set aside.
Add the chicken broth, olive oil, and rice to the pot and bring to a boil, then reduce heat to a simmer.
Cover tightly and cook for 6 minutes.
Add the broccoli and replace the cover. Cook for 9 more minutes, or until no liquid remains in the pot and the rice is cooked through.
Turn off the heat and leave the cover on. Let the rice stand for 10 minutes, do not stir.
Add the cooked chicken, cream of chicken soup, milk, sour cream, optional seasonings, and half of the cheddar cheese to the pot of rice.
Add to a lightly greased 9 x 13 casserole dish and top with remaining cheese.
Cover and bake for 15 minutes.
Melt the butter and crush the crackers. Combine to form the topping for the casserole.
Sprinkle the crumbled cracker topping over the casserole and bake uncovered for 10 additional minutes.
Let stand for 5 minutes prior to serving.