1. Preheat oven to 425° F. Combine the mirin, soy sauce, and white and red miso in a small bowl, stirring, until the miso dissolves. Set the seasoning aside.
2. Heat a clay pot over medium heat. Add the oil, swirling to coat sides. Add the onion, ginger, and garlic and cook until onions begin to brown, about 5 minutes. Add the chicken, carrots, parsnips, radish, chicken broth, water, and seasoning. Bring to a simmer, then cover, and place into the oven. Roast until chicken is cooked through, about 1 hour.
3. Garnish with green onion and serve with steamed rice.
