Add potatoes, carrot, celery, onion, broth, and salt to a large pot. Bring to a boil.
Reduce heat and simmer 15–20 minutes, until potatoes are fork-tender.
Mash potatoes in the pot to your preferred texture (chunky or smooth).
In a bowl, whisk together melted butter, flour, and milk until smooth.
Slowly pour the milk mixture into the pot, stirring constantly.
Simmer 5–8 minutes, stirring often, until thickened.
Stir in parsley, pepper, shredded cheese, and cooked bacon.
Serve hot with extra cheese and bacon on top or ladle into bread bowls.