Preheat oven to 350°F (175°C).
Prepare chicken: Cut chicken into bite-sized pieces and season with Italian seasoning, salt, and pepper.
Cook chicken: In a large pot over medium heat, melt butter and cook the chicken until golden, about 5 minutes. Remove and set aside. (Skip this step if using rotisserie chicken.)
Cook the rice: In the same pot, add chicken broth, olive oil, and uncooked rice. Bring to a boil, reduce to a simmer, cover, and cook for 6 minutes.
Add broccoli: Stir in the broccoli, cover again, and cook for another 9 minutes or until rice is tender and liquid absorbed. Simmer an extra 5 minutes if needed.
Rest the rice: Remove from heat and let the rice sit, covered, for 10 minutes to finish steaming.
Mix it up: Stir in the cooked chicken, cream of chicken soup, milk, sour cream, half the shredded cheese, and any optional seasonings.
Assemble the casserole: Transfer the mixture to a greased 9x13-inch baking dish. Top with remaining cheese, cover with foil, and bake for 15 minutes.
Add the topping: Mix crushed Ritz crackers with melted butter. After 15 minutes of baking, uncover the casserole, sprinkle on the topping, and bake uncovered for another 10 minutes until golden and bubbly.
Cool and serve: Let rest 5 minutes before serving.