Heat the butter in a large pot on medium high heat. Once melted, add in the carrot, onion, celery and parsley and cook, stirring frequently, for 5 mins.
Add in the parsley and flour and cook, stirring constantly, for 2 minutes.
Add in the potato, broth, milk and salt. Bring to a boil and boil 2 minutes. Then, Cover, reduce to low and simmer 25 minutes.
Finally, remove the lid and bring to a boil for 2 more minutes, until it just starts to thicken.