Preheat oven to 350°F. Cut chicken into bite sized pieces and season with salt, pepper, and Italian seasoning.
Heat butter in a large pot over medium heat. Add chicken and cook until golden brown, about 5 minutes. Remove chicken and set aside.
Add chicken broth, olive oil, and rice to the pot. Bring to a boil, then reduce heat to a simmer. Cover tightly and cook for 6 minutes.
Add broccoli and replace the cover. Cook for 9 more minutes, or until no liquid remains and rice is cooked through. If rice is not fully cooked, cover and simmer 5 more minutes.
Keep covered and remove from heat. Let rice stand for 10 minutes without stirring.
Add cooked chicken, cream of chicken soup, milk, sour cream, optional seasonings, and half of the cheddar cheese. Stir to combine.
Transfer to a lightly greased 9x13 inch casserole dish and top with remaining cheese. Cover and bake for 15 minutes.
Combine melted butter and crushed crackers. Sprinkle over casserole and bake uncovered for 10 more minutes. Serve hot.