Preheat your oven to 250°F (120°C).
Place all of the prepared onions, garlic, celery, carrots, leftover vegetables, herbs, and wild rice at the bottom of a 6qt Dutch oven. If using regular rice, save the rice for after the stew is cooked.
Add the bird carcass to one side of the Dutch oven, and place additional meat on the other side of the Dutch oven.
Season generously with salt and pepper.
Add the bone stock or water to the Dutch oven.
Cover the Dutch oven with a lid and cook the stew in the oven for five hours.
After five hours, add the peas and cooked rice (if using), and cook for another fifteen minutes.
Use a fork to shred the remaining meat off the bones. Carefully remove all bones from the stew.
Season with additional salt or pepper to taste if needed. Allow the stew to cool for fifteen minutes before serving.