Gather all ingredients.

Bring broth, onion, carrots, celery, garlic, and salt to a boil in a large saucepan or small Dutch oven over high heat; reduce heat to medium-low and simmer until vegetables are softened, about 10 minutes. Using a slotted spoon, transfer vegetables and 1 cup of broth to a blender.

Secure lid on blender, remove center piece to allow steam to escape, and place a clean towel over the opening. Process until smooth, about 30 seconds. Stir blended vegetable mixture back into soup.

Add thyme sprigs, bay leaves, and a Parmigiano-Reggiano cheese rind to the soup. Bring to a boil over medium-high heat. Add pasta, reduce heat to medium-low, and simmer, stirring occasionally, until pasta is tender, 18 to 20 minutes. Add shredded chicken in the last 3 minutes of cooking.

Remove from heat and discard thyme sprigs, bay leaves, and Parmigiano-Reggiano cheese rind.