Bring a large pot of salted water to a boil. Carefully drop in the Agnolini and cook until they float to the surface, about 2-3 minutes. Remove with a slotted spoon and set aside.
In a separate pot, combine the chicken or beef broth with the chopped carrot, celery, and onion. Season with salt to taste.
Bring the broth to a simmer and let it cook for about 30 minutes, allowing the flavors to meld.
Place a few cooked Agnolini in serving bowls. Ladle the hot broth over the Agnolini.
Garnish with freshly grated Parmesan cheese and a sprinkle of chopped parsley, if desired.
