Set your oven to 350°F to preheat.
Cut the chicken into small pieces and toss with salt, pepper, and Italian seasoning.
Melt butter in a large pot over medium heat and cook the chicken pieces until they turn golden, about 5 minutes; then remove the chicken and set it aside.
Pour chicken broth, olive oil, and rice into the same pot and bring it to a boil; reduce heat to low, cover tightly, and simmer for 6 minutes.
Add the broccoli florets, cover again, and let cook for another 9 minutes or until the rice has absorbed all the liquid and is tender. If needed, cover and cook an additional 5 minutes.
Remove the pot from heat and let the rice rest, covered, for 10 minutes without stirring.
Stir in the cooked chicken, cream of chicken soup, milk, sour cream, optional thyme and garlic powder, and half of the shredded cheddar cheese.
Transfer the mixture into a greased 9x13 inch casserole dish and sprinkle the remaining cheddar cheese on top. Cover and bake for 15 minutes.
Mix the melted butter with the crushed Ritz crackers and spread this crumb topping over the casserole.
Bake uncovered for 10 more minutes until the topping is golden and crispy. Serve warm.
