In a large pot, heat the olive oil over medium heat.
Add the onion, carrots, and celery. Sauté for 5–7 minutes until soft.
Stir in the garlic and cook for 1 minute, just until fragrant.
Pour in the chicken broth, then add the Parmesan rind, thyme, and bay leaves. Bring to a boil, then reduce to a simmer for 15 minutes.
Remove about half the vegetables and blend until smooth. Return to the pot.
Stir in the pastina and cook for 7–9 minutes until tender.
Add the chicken and spinach if using. Simmer for 3 minutes. Remove the rind and herbs. Stir in Parmigiano-Reggiano, lemon juice, salt, and pepper.
Sprinkle with parsley and serve warm.