Add broth, garlic, onion, carrots, celery, bay leaves, bouillon, salt + pepper to a large pot. Bring to a boil, then cover and reduce heat and let simmer for 45 minutes, until the veggies are fork-tender.
Cook the pastina according to package directions. Drain, toss with butter and the 1/2 cup Parmesan and set aside.
Remove the veggies and blend with 2 cups of broth until completely smooth in a blender or use an immersion blender.
Stir the veggie purée back into the remaining broth.
Add pastina to your bowl, ladle the soup over top, and finish with more Parmesan and some fresh cracked black pepper.