It's easy, it's delicious, and it only has three ingredients (and a little butter, salt and pepper)
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Start with 4 medium potatoes- Idahos, Yukon golds- whatever you like- and a couple of good sized leeks. Your potatoes are smaller than these? Use more. Don't worry too much about quantities.
First step is cleaning the leeks. Notice I've trimmed around the leeks, removing the dark green parts, and leaving the white and light green parts.
Using a sharp knife, slit the leaks from the green end down to to the root end, but don't cut through. Rinse under running water,. Leeks tend to collect mud in between the layers, and you want to make sure you get all of it out.
Chop the leeks coarsely.
Peel the potatoes and cut into 1" or smaller pieces.
Coarsely chop the leeks. (Leaving them attached at the root end makes this much easier.)
Melt two or three tablespoons of butter in a large saucepan and add the leaks. Cook over moderate heat until the leek pieces are well softened.
Add the potatoes that you've peeled and cut into small chunks, along with chicken or vegetable stock- about half a quart for the amount of leeks and potatoes used here. You can add more later if the soup's too thin. Simmer, stirring occasionally to make sure nothing;s sticking to the bottom of the pot.
When the potatoes are fully cooked (you should be able to squish them with a fork) puree the soup with your hand blender, a regular blender, or a food mill. In a pinch you could just mash it up with a big fork, especially if you liked your soup with a coarser texture.
Taste your soup, and add salt and pepper if needed. Add more stock, or water, if the soup's too thick. Serve and enjoy.