Preheat your oven to 350°F (175°C). Grease a 9x13-inch baking dish with cooking spray or olive oil.
In a large skillet, heat the olive oil over medium heat. Add the chopped onion, celery, and mushrooms. Sauté for about 5-7 minutes until the vegetables are softened.
In a large mixing bowl, combine the cooked wild rice, shredded chicken, sautéed vegetables, frozen peas, cream of mushroom soup, chicken broth, garlic powder, onion powder, thyme, salt, and pepper. Mix well until all ingredients are evenly combined.
Pour the mixture into the prepared baking dish and spread it out evenly.
Sprinkle the shredded cheddar cheese over the top of the casserole.
In a small bowl, mix the crushed buttery crackers with a tablespoon of melted butter (optional) and then sprinkle over the cheese layer.
Cover the baking dish with aluminum foil and bake in the preheated oven for 25 minutes. Remove the foil and bake for an additional 15-20 minutes, or until the casserole is bubbly and the topping is golden brown.
Allow the casserole to cool for about 5-10 minutes before serving.