Preheat the oven to 350°F.
Cut the chicken into bite-sized pieces and season with Italian seasoning, salt, and pepper.
In a large skillet, melt butter over medium heat and cook the chicken until golden brown on all sides, about 5 minutes, then remove and set aside. (Skip this step if using cooked rotisserie chicken.)
Put this chicken in pot and to the same pot, add chicken broth, olive oil, and rice.
Bring to a boil, then reduce heat, cover tightly, and simmer for 6 minutes.
Add the broccoli, replace the lid, and continue cooking for 9 more minutes until the rice is tender and the liquid is absorbed.
Remove the pot from heat and let it sit, covered, for 10 minutes without stirring to allow the rice to release.
Add the cooked chicken, cream of chicken soup, milk, sour cream, optional seasonings, and half of the cheddar cheese to the rice mixture and stir to combine.
Transfer to a greased 9 x 13-inch casserole dish, top with remaining cheese, cover, and bake for 15 minutes.
Meanwhile, melt butter and crush crackers, then mix together in a small bowl to make the topping.
Sprinkle the topping evenly over the casserole and bake uncovered for an additional 10 minutes.
Let the casserole rest for 5 minutes before serving.