Put onion, carrots, celery, garlic, chicken, broth, salt and pepper in a large pot. Bring to a gentle simmer.
Cook for 20 to 25 minutes until the vegetables are soft and the chicken reaches 165°F. Remove the chicken to a plate.
Blend the vegetables and broth smooth with an immersion blender, keeping its head submerged to avoid splashing. Return the soup to a gentle simmer.
Add pastina and cook for 6 to 8 minutes, or its package time, stirring frequently. Finely shred the chicken and return it to the pot.
Remove from the heat and stir in Parmesan and butter until melted. Serve while the tiny pasta remains suspended in a pourable broth.