Sauté Vegetables: Add oil to a 4-quart Dutch oven or soup pot and heat over medium-high heat. Add carrots, celery, and onion. Cook until onions are translucent, about 3-4 minutes.
Add Seasonings: Add salt, garlic, parsley, thyme, and pepper. Cook for 1 minute.
Add Broth and Chicken: Pour in the broth, scraping the bottom of the pot. Add the chicken breasts and simmer for 10 minutes. Remove chicken to shred.
Cook Pasta: Stir in pasta, cover, and simmer for 10 minutes or until pasta is al dente.
Finish Soup: Whisk together cream and corn starch. Stir into the soup with shredded chicken. Cook until thickened. Adjust salt and pepper before serving.