Place all the vegetables in a medium pot, and add the salt and the water to cover. Cover and bring to a boil over high heat. Reduce heat to medium-low and cook, covered, for about 30 minutes, or until the potatoes break easily when pierced with a knife, and carrots and celery are tender.

Remove the pot to the side, and using a stand mixer purée the vegetables in the pot. Add the milk and butter and continue pureeing for a few seconds. Return pot to the cooking ring and cook over medium-low heat for few minutes. Add a bit of hot water if too thick, and adjust taste if required. Serve hot with a slice of rustic bread.