Prepare the oven and chicken. Preheat the oven to 350°F (175°C). Cut the chicken breasts into bite-size, approximately 1-inch pieces, then season them lightly with salt and black pepper.

Cook the chicken and vegetables. Melt 2 tablespoons of butter in a large Dutch oven or sturdy pot over medium heat. Add the chicken pieces, diced onion, and chopped celery. Toss everything in the melted butter and sauté for about 3 minutes, until the chicken is approximately halfway cooked.

Add the broccoli. Place the broccoli florets into the pot and drizzle in 1 tablespoon of olive oil. Continue cooking for another 3–5 minutes, or until the chicken has cooked completely through. Remove the pot from the heat.

Assemble the creamy filling. Add the cream of chicken soup, sour cream, milk, garlic powder, onion powder, mustard powder, and half of the shredded cheddar cheese to the chicken and vegetables. Stir thoroughly until the ingredients are evenly incorporated.

Transfer to the baking dish. Lightly grease a 9 × 13-inch casserole dish. Spoon the chicken and broccoli mixture into the prepared dish and spread it evenly. Scatter the remaining cheddar cheese across the top.

Complete the first bake. Cover the casserole dish with aluminum foil and bake at 350°F (175°C) for 20 minutes. Remove the casserole from the oven after baking and raise the oven temperature to 400°F (205°C).

Prepare the buttery cracker topping. While the oven is heating to the higher temperature, combine the crushed Ritz crackers with 2 tablespoons of melted butter in a small bowl. Mix until the crumbs are evenly coated.

Finish baking. Sprinkle the buttered cracker crumbs evenly over the casserole. Return the uncovered dish to the oven and bake for another 8–10 minutes, until the topping develops a golden-brown finish.

Rest before serving. Remove the casserole from the oven and allow it to stand for 5 minutes so the filling can settle. Serve hot with rice, biscuits, or mashed potatoes.