Preheat the oven to 350° F.
Lightly grease a 13x9-inch casserole dish with butter. Set aside until needed.
Pat the chicken breasts dry with paper towels.
Cut chicken into bite-sized pieces.
Season the pieces with salt and black pepper.
Add the olive oil to a large pot (about 6 qt) or deep skillet over medium heat.
When the oil is hot, add the chicken pieces and cook for 4-5 minutes, turning the pieces to sear all of the sides. Remove the pieces from the pan and set aside until needed.
Add the chicken broth, butter, and rice to the pot, and bring to a boil, then reduce heat to a simmer.
Place a lid on the pot and cook for 6-8 minutes.
Add the broccoli florets on top, do not stir the mixture, and replace the cover.
Cook for 8-10 minutes, or until no liquid remains in the pot.
Remove the pan from the heat, leaving the cover on. Let the mixture stand for 8-10 minutes, do not stir.
Add the cooked chicken, cream of chicken soup, whole milk, sour cream, one cup of shredded cheddar cheese, garlic powder, onion powder, and black pepper to the pot.
Gently stir the mixture to combine.
Pour the rice mixture into the prepared casserole dish.
Sprinkle the remaining shredded cheddar cheese on top of the mixture.
Lightly cover the casserole dish with aluminum foil, and place it on the center rack of the preheated oven and bake for 15 minutes.
Place the ritz crumbs in a bowl and drizzle the melted butter over them, tossing to combine.
Sprinkle the crumbled cracker topping over the casserole and bake uncovered for 8- 12 minutes until the crackers begin to brown and the internal temperature of the casserole is at least 165 degrees F.
Le the casserole stand for 5-7 minutes before serving, so it can set up a bit.