Place the chopped onion, carrot, and celery in a large pan with two tbsp of olive oil. Stir until the onion is translucent and the carrots are golden. Stir in the garlic.
Chop each chicken breast into 3-4 pieces and add them to the sauteed veggies.
Add the broth, ground dried thyme, pepper, bay leaves, and salt.
Bring the soup to a boil and then reduce the heat. Simmer for 5-8 minutes or until chicken is cooked through.
Keep the soup on low heat, and once the chicken is cooked, remove the chicken from the soup and place it onto a plate or cutting board, then use a fork and a knife to separate chicken. When you finish shredding the chicken, return it back to the soup pot.
Add the dry pasta and cook it following its package directions.
Once the pasta is ready, mix milk, grated parmesan, and cornstarch in a small bowl and add then add the mixture to the soup.
Stir for two minutes and turn off the stove. Taste test for saltiness and adjust.
Serve warm with fresh parsley on top.