Steam rice: I was able to steam the wild rice and white rice together. Add the wild rice to the saucepan with two cups of water over medium heat. Simmer, loosely covered, or 10 minutes to give the wild rice a head start. After the wild rice has been steaming for 10 minutes, add the white rice and cook for another 15-20 minutes. Stir occasionally so it doesn't burn to the bottom and taste test consistency when most of the liquid is evaporated. Add more water and steam longer if rice is too chewy.
Preheat oven to 350℉. Heat oil into a medium pot or deep skillet over medium heat. Sauté onion, celery and carrots until softened, about 10 minutes. Stir in garlic and cook for 1 minute. Stir in chicken, both rices, salt, and pepper.
To prepare cheese sauce: Melt butter into a medium saucepan over medium high heat. Whisk in flour, salt and pepper, then slowly pour in chicken stock, stirring continuously. Stir until thick and nearly boiling, then stir in ¾ cup cheddar cheese until melted. Pour cheese sauce into cooked rice mixture, then transfer to a 8x8 inch baking dish. Top with the rest of the cheese and bake for 25-30 minutes, or until cheese is melted through.
Allow the casserole to sit for 5-10 minutes before serving.