Lightly grease a 9x13-inch casserole dish with olive oil and set aside.

Combine the chicken broth, olive oil, and rice in a large pot. Bring to a boil, then reduce the heat to a simmer. Cover tightly and cook for 7 minutes.

Add the broccoli and replace the lid, cook for 8 minutes more without stirring.

Turn off the heat and leave the lid on the pot. Let the rice stand for 10 minutes, without stirring. The steam will cause any rice stuck to the bottom of the pot to release, there is no need for you to stir. 

Preheat the oven to 350F. 

Mix the sour cream and the crumbled bouillon cube together. Add the sour cream mixture, chicken, Italian Seasoning, milk, garlic powder, and 1 cup of cheddar cheese to the cooked rice and broccoli. Stir to combine. Taste then season with coarse kosher salt and black pepper to your liking.

Pour this mixture into the prepared baking dish, top with the remaining 1 cup of shredded cheddar cheese then cover with foil and bake for 15 minutes.

Meanwhile, melt the butter and crush the crackers then combine them together to create the topping. 

After the initial bake time, remove the foil, sprinkle the cracker topping over the top of the casserole, and sprinkle the Piment d'Ville chile powder or smoked paprika across the top. 

Bake for an additional 10 minutes. Then let the casserole rest for 5 minutes before serving.