Preheat oven to 300 degrees F. Rinse the chicken well with cold water and place in a deep ovenproof roasting pan with the onion, carrot, celery, tomato and bay leaf. Add enough cold water to come up about 2/3 the sides of the bird. Bring to a simmer on top of the stove, straddling two burners if necessary. Cover, place in the oven and braise until the chicken is completely cooked (about 1-1/2 hours).
Remove from the oven and turn the chicken over in the broth to cool. Remove the cooled chicken from the broth. Shred the chicken and strain the broth into a stockpot. Reserve.
Bring a pot of salted water to boil. Add the Pastina and cook for about 15 minutes or until done. Drain and set aside. Bring the reserved broth to a simmer, season with salt and pepper and add the cooked Pastina. Add the chicken and greens in order to wilt the greens and heat the chicken. Ladle into bowls. Grate Parmesan over the soup and finish with freshly-cracked pepper.