In a large pot, melt butter over medium heat. Add onion, carrots, and celery, and sauté until softened, about 5 minutes.
Stir in garlic and cook for another minute.
Pour in the chicken broth, then add the shredded chicken, thyme, parsley, salt, and pepper. Bring to a boil, then reduce heat and simmer for 10 minutes.
Add egg noodles and cook according to package instructions, about 8 minutes.
In a separate bowl, whisk together heavy cream, flour, and milk until smooth. Gradually stir into the soup, cooking for another 5 minutes until thickened.
Taste and adjust seasoning if needed. Serve hot, garnished with fresh parsley.