Melt butter in a 6 quart dutch oven or large soup pot over medium high heat. Add carrots, onion and celery. Cook for 4 minutes, stirring frequently. Add garlic and cook until fragrant (about 30 seconds).
Add chicken broth, water, cream of chicken soup, dill, rosemary, salt, pepper, cooked chicken and bay leaves. Stir to combine.
Increase heat to high and bring to a boil. Add noodles and stir to combine. Reduce heat as necessary to maintain a gentle boil (medium high to medium). Boil gently for 8 minutes (stirring occasionally), or until noodles and vegetables are tender.
Remove and discard bay leaves. Season with additional salt and pepper, if desired.
Sprinkle with chopped fresh parsley, if desired.