Chop bacon and fry in a frying pan until oil is rendered. Set aside. Scrub the potatoes, and cut them into 1- inch chunks. Place them in a saucepan with the leeks,celery, carrots and butter. Add salt. Cook the vegetables , stirring over medium heat, until the butter is melted and all the particles are coated( 5min).
Add the stock or water, bring to a boil, then cover, and reduce the heat to a simmer. Coat until the potatoes are soft(20-30 min). Check the moisture level occasionally, You may need to add a little extra stock or water if it gets too low.
When the potatoes are tender, remove the pan from the heat, and puree its contents in the milk( I use an immersion blender but you could also use a standard blender or food processor). Make sure the mixture is utterly smooth. retuen it to the saucepan.
Add optional herbs( or not). Grind in some black pepper to your taste.
Serve right away