Place potatoes into a large saucepan with water to cover. Bring to a boil and cook until tender. Meanwhile, saute leeks in butter until translucent.
When potatoes are done, skin them while they are still hot and cut them into bite sized pieces. Place potatoes into a stock pot with chicken broth and leeks. season with salt and pepper. Cook over medium heat until simmering, then remove from heat and stir in milk. Serve immediately.