1Place chicken in 12-inch skillet. Add 1 carton of the broth. Heat to boiling. Reduce heat; cover and simmer 20 minutes or until juice of chicken is clear when center of thickest part is cut (170°F).
2Meanwhile, in 5-quart stockpot, heat oil over medium heat. Add onion, carrot and celery; cook 8 to 10 minutes, stirring occasionally, until vegetables are tender.
3Drain chicken, reserving broth; set chicken aside. Strain broth; add to vegetables. Stir remaining carton of broth, the tomatoes, salt, pepper and bay leaf into stockpot. Heat to boiling. Stir in pasta. Reduce heat; cover and simmer 15 minutes.
4Shred or cut chicken into bite-size pieces; add to soup. Stir in greens just until wilted. Remove bay leaf. Serve with a sprinkle of additional freshly ground pepper and the cheese.