Preheat oven to 350 degrees F
Cut chicken into small pieces and season with Italian seasoning, garlic powder, and salt and pepper to taste.
Add the chicken broth, olive oil, and rice to the pot and boil, then reduce heat to a simmer.
Tightly cover and cook for 7 minutes.
Add the broccoli and replace the cover. Cook for 8 more minutes. Do not stir.
Turn the heat off and leave the pot covered. Let the rice stand for 10 minutes without stirring.
Add the cooked chicken, soup, milk, sour cream, and half of the cheddar cheese.
Transfer to a lightly greased 9 x 13 casserole dish. Top with remaining cheese.
Cover and bake for 15 minutes.
Melt the butter and crumble up the crackers. Combine to form the topping for the casserole.
Top the casserole with the crumbled cracker topping and bake uncovered for 10 additional minutes.