Season the chicken with Italian seasoning, salt, and pepper to taste, then cut into bite-sized pieces.
In a large saucepan, melt the butter over medium heat. Cook, stirring occasionally, for approximately 5 minutes, or until the chicken is browned on both sides. Take out and place aside. The use of a cooked rotisserie chicken eliminates the requirement for this step.
Before reducing heat to a simmer, add the rice, chicken stock, and olive oil to the saucepan and bring to a boil.
Secure the lid and cook for seven minutes.
If using fresh broccoli, add it now and put the lid back on. Additional 8 minutes of cooking time is required. Hold your breath.
Take the lid off and turn off the stove. Do not stir the rice; let it stand for 10 minutes. There will be no sticking rice left in the pot.
Combine the cooked chicken with the soup, milk, sour cream, half of the cheddar cheese, and any seasonings you like.
Layer in a 9 by 13 casserole dish that has been gently oiled, then sprinkle with the remaining cheese.
After 15 minutes of covering, bake.
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