1. Bring chicken and water to cover to a boil in a Dutch oven over medium-high heat; reduce heat to low, and simmer 1 hour.
2. Remove chicken, reserving liquid, and let cool 15 minutes. Shred chicken.
3. Pour reserved cooking liquid through a wire-mesh strainer into a bowl, discarding solids; wipe Dutch oven clean. Add water to cooking liquid to equal 10 cups.
4. Sauté onion, celery, and garlic in hot oil in Dutch oven over medium-high heat 5 to 6 minutes or until tender. Add shredded chicken, cooking liquid, carrots, and next 3 ingredients. Cover, reduce heat to medium, and cook 20 minutes or until carrots are tender. Add parsley. Serve with desired toppings.