Heat the olive oil over medium heat in a large soup pot, add the onion, carrots, celery, and 1 teaspoon each salt and pepper. Cooking, stirring frequently, until the vegetables are soft, about 15 minutes. Add the garlic and cook about 1 minute. Add chicken stock and bring to a boil.
Add the noodles and cook 6 minutes, then add the chicken and cook another 2 minutes, until the noodles are cooked through and the chicken is warm. Season to taste with salt and pepper, then stir in the parsley. Serve topped with Parmesan.