Preheat your oven to 350°F (175°C).
Cut the chicken into small, bite-sized pieces and season lightly with salt and pepper.
In a large pot or Dutch oven, melt the butter over medium heat. Add the diced onion, celery, and chicken pieces, tossing to coat evenly. Sauté for about 3 minutes until the chicken is partially cooked. Then, add the broccoli florets and a tablespoon of olive oil. Continue cooking for an additional 3-5 minutes until the chicken is thoroughly cooked through. Remove 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. Mix well to combine all ingredients thoroughly.
Transfer the mixture to a lightly greased 9x13-inch casserole dish, spreading it out evenly. Sprinkle the remaining shredded cheese over the top.
Cover the casserole dish with foil and bake in the preheated oven for 20 minutes. Afterward, remove the foil and increase the oven temperature to 400°F (200°C).
In a small bowl, combine the melted butter with the crushed Ritz crackers or panko breadcrumbs. Sprinkle this mixture over the top of the casserole. Return to the oven and bake for an additional 8-10 minutes, or until the topping is golden brown and crispy.
Allow the casserole to rest for 5 minutes before serving.
This dish is perfect when served over rice, biscuits, or mashed potatoes.