You will need:
Potatoes (russet or Yukon Gold), about five pounds for a lot of soup, peeled and cut into 1″ cubes
Butter, olive oil, bacon fat
Leeks (usually sold in bundles of three at our local store)
Stock (at least one carton), chicken or vegetable
White Pepper (or black if you don’t mind the color)
Green onions or chives
As a fungible recipe, you can increase the amounts of the vegetables you desire in order to change the flavor profile to your own taste.
In a large pot, heat a significant amount—at least 1/4 cup—of butter, olive oil, bacon fat, or some combination over medium heat. Chop up the leeks, then the carrots and celery, where the amounts of the carrot and the celery are about half that of the leek. Drop into the pot and salt; cook, stirring gently, until the vegetables start to soften. Add the peppers and cook for a couple of minutes; add the mushrooms and cook briefly.
Pour the entire contents of the carton of stock into the pot and blend. (We use an immersion blender; it is possible to use a tabletop blender if you do it in rounds.) Add the potatoes and enough water to just cover them. Simmer, partially covered, for at least 45 minutes or until potatoes are tender.
Use a slotted spoon to remove a couple of cups of potato cubes; set aside. Blend the rest, adding milk until desired consistency is reached. Add salt and white pepper to taste. Stir potato chunks back into the soup; serve with green onions or chives on top.
Leftovers can be stored for several days in the refrigerator.