In a large soup pot, combine chicken, carrots, parsnips, celery, onions, bay leaves, garlic, peppercorns, and 1 teaspoon coarse salt. Add water to cover by 2 inches. Bring to a boil, reduce heat to medium. Simmer partly covered, occasionally skimming and discarding fat from surface, about 1 hour.
With a slotted spoon or tongs, remove chicken, carrots, and parsnips from pot; set aside. Pour remaining contents of pot through a fine-mesh sieve into another large pot; discard solids, and bring broth to a boil. Add rice and white part of scallions. Reduce heat to medium, and simmer, uncovered, until rice is tender, about 20 minutes.
Meanwhile, remove chicken from bones, and shred into bite-size pieces (discard any fatty or discolored parts). Cut carrots and parsnips into bite-size pieces. When rice is cooked, return chicken, carrots, and parsnips to broth in pot; add green part of scallions. Season generously with 5 to 6 teaspoons coarse salt.