Preheat your oven to 350°F (175°C).
In a large mixing bowl, combine the cooked rice, shredded chicken, frozen peas, and shredded cheddar cheese.
In a separate bowl, whisk together the condensed cream of mushroom soup, sour cream, milk, chopped onion, minced garlic, salt, black pepper, dried thyme, and paprika until smooth.
Pour the soup mixture over the rice and chicken mixture and stir until all ingredients are evenly combined.
Transfer the mixture into a greased 9×13-inch casserole dish and spread it out evenly.
In a small bowl, mix the melted butter with the crushed buttery crackers.
Sprinkle the cracker topping evenly over the casserole.
Cover the dish with aluminum foil and bake for 30 minutes.
Remove the foil and bake for an additional 15 minutes, or until the topping is golden brown and the casserole is heated through.
Let the casserole rest for 5 minutes before serving.