In a large saucepan or small Dutch oven, bring the chicken broth, onion, carrots, celery, garlic, and salt to a boil over high heat.
8 cups lower-sodium chicken broth, 2 cups chopped sweet onion, 1½ cups peeled and coarsely chopped carrots, 2 coarsely chopped celery ribs, 6 garlic cloves, ¾ teaspoon salt
Reduce the heat to medium-low and simmer for about 10 minutes, until the vegetables are tender.
Use a slotted spoon to transfer the vegetables and 1 cup of the broth to a blender.
Remove the center of the lid to allow steam to escape, blend until smooth (about 30 seconds), then stir the purée back into the pot. Add the thyme sprigs, bay leaves, and cheese rind.
4 thyme sprigs, 2 fresh bay leaves, 1 2-ounce Parmigiano-Reggiano cheese rind
Bring the soup back to a boil over medium-high heat. Add the pasta, then reduce the heat to medium-low and simmer for 8 to 10 minutes, stirring occasionally, until the pasta is tender.
½ cup uncooked pastina pasta
Stir in the shredded chicken during the last 3 minutes of cooking.
2 cups shredded rotisserie chicken
Remove from the heat and discard the thyme sprigs, bay leaves, and cheese rind.
Serve hot, topped with chopped parsley and grated Parmigiano-Reggiano.
Fresh flat-leaf parsley