Preheat your oven to 350°F (175°C).
Season the diced chicken with a light sprinkling of salt and pepper.
In a large pot or Dutch oven, melt 2 tablespoons of butter over medium heat. Add the chicken, diced onion, and celery, stirring to coat. Sauté for about 3 minutes until the chicken is halfway cooked, then add the broccoli and 1 tablespoon of olive oil.
Continue cooking for another 3-5 minutes until the chicken is cooked through. Remove the pot from heat.
Stir in the cream of chicken soup, sour cream, milk, garlic powder, onion powder, mustard powder, and half of the shredded cheddar cheese until well combined.
Transfer the mixture into a lightly greased 9x13-inch casserole dish. Sprinkle the remaining cheddar cheese over the top.
Cover the casserole and bake for 20 minutes. Then, increase the oven temperature to 400°F (200°C).
In a small bowl, combine the melted butter and crushed Ritz crackers. Remove the cover from the casserole, sprinkle the cracker mixture over the top, and bake for an additional 8-10 minutes until the topping is golden brown.
Allow the dish to sit for 5 minutes before serving.
Serve over rice, biscuits, or mashed potatoes.