Cook the Chicken: In a large pot, bring the chicken broth to a boil over high heat. Add the chicken breasts and reduce heat to medium-low. Simmer for 15-20 minutes until chicken is cooked through. Transfer chicken to a plate and shred or dice it once cool enough to handle.
Sauté the Vegetables: In the same pot, heat the olive oil over medium heat. Add the onion, carrots, and celery. Sauté for 5-7 minutes until vegetables begin to soften.
Build the Soup: Add the garlic and sauté for 1 minute until fragrant. Pour in the chicken broth and add the Parmesan rind, bay leaves, and thyme. Bring to a gentle boil.
Cook the Pastina: Once boiling, add the pastina to the pot. Reduce heat to medium-low and simmer for 8-10 minutes, stirring occasionally, until the pasta is tender.
Finish the Soup: Remove the bay leaves and Parmesan rind. Stir the shredded chicken back into the soup. Season with salt and pepper to taste.
Serve: Ladle the hot chicken pastina soup into bowls. Garnish with chopped fresh parsley.