Preheat oven to 350°F (175°C). Cut chicken into bite-sized pieces and season with salt, pepper, and Italian seasoning.
In a large pot, melt butter over medium heat. Add chicken and cook until lightly golden (about 5 minutes). Remove and set aside.
Add chicken broth, olive oil, and uncooked rice to the same pot. Bring to a boil. Reduce heat to low, cover tightly, and simmer for 6 minutes.
Add broccoli to the pot, cover again, and cook for 9 more minutes until rice is tender and liquid is absorbed.
Turn off heat and let the pot sit covered for 10 minutes without stirring.
Stir in the cooked chicken, cream of chicken soup, milk, sour cream, half of the shredded cheese, and any optional seasonings. Mix until combined.
Transfer mixture into a greased 9x13-inch casserole dish. Top with remaining cheese. Cover and bake for 15 minutes.
Mix crushed Ritz crackers with melted butter. Uncover the casserole, sprinkle the topping, and bake for an additional 10 minutes or until golden and bubbly.
Let rest a few minutes before serving.