In a large soup pot, combine split peas, carrots, celery and 1 onion with water. Bring to a boil. Stir in barley, bay leaf and garlic, if using. Reduce heat and simmer partly covered for 1 1/2 to 2 hours. Stir occasionally. Add salt and pepper to taste.
In a nonstick skillet, heat oil. Saute the remaining 2 onions on medium heat until well-browned, about 6 to 8 minutes. Add onions to soup along with dill. Simmer soup 5 to 10 minutes longer. Discard bay leaf (and turkey carcass, if using).