1. In 8-quart Dutch oven or saucepot, combine chicken, onion, peppercorns, bay leaf, and 12 cups water; heat to boiling over high heat. Reduce heat to low; cover and simmer 1 hour and 15 minutes or until chicken is tender.
2. Meanwhile, prepare meatballs: In large bowl, with hands, combine ground meat, garlic, egg, parsley, pepper, 1/2 cup Romano cheese, and 3/4 teaspoon salt. In small bowl, mix bread crumbs and milk to form a thick paste. Mix bread-crumb mixture into meat mixture just until blended. Shape meat mixture into about seventy 1-inch meatballs and place on cookie sheet; cover and refrigerate 30 minutes.
3. Remove chicken to bowl; cool until easy to handle. Discard skin and bones from chicken; cut chicken into bite-size pieces. Reserve 2 cups cut-up chicken; refrigerate remaining chicken for use another day. Pour chicken broth through sieve lined with paper towels into large bowl. Let stand a few seconds until fat separates from meat juice. Skim fat from broth and discard.
4. Return broth to clean Dutch oven or saucepot; add canned chicken broth and 2 teaspoons salt; heat to boiling over high heat. Stir in carrots and celery; heat to boiling. Reduce heat to low; cover and simmer 8 to 10 minutes, until vegetables are tender. Add meatballs and 1/4 cup Romano cheese; heat to boiling over high heat. Reduce heat to low; cover and simmer 15 minutes or until meatballs are cooked through. Stir in escarole and reserved chicken; heat through. Serve with grated Romano cheese to sprinkle over each serving.