In a large saucepan, combine the chicken, halved onion, garlic, bay leaf and enough water to cover. Bring to a boil, then lower the heat and simmer gently until the chicken is cooked through, 15 to 20 minutes.
While the chicken is cooking, in a soup pot or Dutch oven, heat the EVOO, 2 turns of the pan, over medium heat. Add the chopped onion, carrots and celery; add the sugar and season with salt and pepper. Cover the pot and cook until the vegetables are softened, about 8 minutes.
Add the chicken broth and 2 cups water to the pot and bring to a boil. Shred the poached chicken into pieces and add to the soup. Stir in the egg noodles and cook until al dente, about 5 minutes. Turn off the heat and stir in the scallions, parsley, dill and lemon peel. Season with salt and pepper.