1. Heat the olive oil until shimmering 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 very soft, about 15 minutes. Add the garlic and cook until fragrant, about 1 minute. Add the stock and bring to a boil.
2. Add the noodles and cook 6 minutes, then add the chicken and cook about 2 minutes more, until the noodles are cooked through and the chicken is warmed through. Season to taste with salt and pepper, then stir in the parsley. Serve topped with Parmesan.
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