Preheat oven to 350 degrees F. Heat oil into a medium dutch oven or pot over medium heat. Saute onion, celery and carrots until softened, about 10 minutes. Stir in garlic and cook for 1 minute. Stir in chicken, both rices, salt, pepper and garlic salt. Reduce heat to low.
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 broth whisking continuously. Whisk until thick and nearly boiling then stir in cheese until melted. Pour cheese sauce into rice mixture then transfer to a 9×13 inch baking dish. Top with additional cheddar cheese and bake for 25-30 minutes or until cheese is melted through.