Simmer the broth. In a large pot with a lid, stir together the broth, onion, carrots, celery, parmesan rind, and a pinch of salt. Turn the heat to high to bring to a boil, then lower the heat and cover. Simmer until the vegetables are very tender, 20 to 30 minutes.
8 cups low-sodium chicken broth, 1 medium yellow onion, 3 medium carrots, 3 celery ribs, 1 parmesan rind, Kosher salt
Puree the vegetables. Discard the parmesan rind, then use a slotted spoon to transfer the vegetables and garlic to a food processor, blender, or use an immersion blender. Add a couple ladles of the broth and blend until the vegetables are fully smooth. Scrape the purreed vegetables back into the pot.
3 cloves garlic
Boil the pasta. Turn the heat to high to bring the broth to a boil. Once boiling, stir in the pastina. Cook until the pasta is tender, about 3 minutes or so. Remove the soup from the heat.
1 1/2 cup pastina or acini di pepe
Serve. Taste the soup and adjust seasoning, adding more salt if it tastes flat. Ladle the pastina into serving bowls. Finish each bowl with a sprinkle of parsley and grated parmesan cheese and serve hot.
1/2 cup finely chopped parsley leaves, Grated parmesan cheese