Here is a recipe for a simple potato leek soup that we made a few weeks ago at school, and that I described a bit here. It uses very few raw materials and they are simply prepared and cooked, and it illustrates a neat cooking process where you use the starch in the potatoes to thicken a soup into something like a light cream soup, even though there is no cream or milk in it. A quick survey of the internet reveals that "Potage Parisienne" always has potatoes and leeks, often some cream, sometimes flour, and occasionally other ingredients to flavor it differently. I would say that the cream is a matter of preference, but the addition of flour should only be needed if the soup is improperly cooked or the potatoes are handled in a way that their starch is lost before it gets into the soup.
You'll no doubt notice that I have a tendency to write volumes to describe how to make even the simplest dishes. While I sympathize with you when you think, "Why does it take all of this to tell me to cut up a leek and some onion, cook them in butter, then add water and sliced potatoes and simmer it awhile?" I don't know a better way to convey to a wide audience the things worth paying attention to if you want to produce a dish that is surprisingly good given how little material and effort goes into it. If you're reading this at all, I assume you are not a professional cook; if you are, you already know how to make a soup like this and what to pay attention to as you go about it. One of the most frustrating things to me as a cook is telling someone about a great dish, and then hearing later that he didn't like it along with a reason for that dislike which indicates that although the prescribed ingredients went into the preparation, they were handled in a way that did not produce the dish that the creator of the recipe had in mind. In other words, the dish was judged and dismissed without ever having been really prepared or sampled.
For 6-8 small cups or 4 small bowls of this soup, you'll need:
1 medium-large or 2 small starchy potatoes (e.g., Idaho; but not small red or yellow boiling potatoes)
1/3 of a medium-large onion, or half or all of a smaller one
1 leek, white and light green parts only
1 Tbsp butter
Water or a light stock, about a quart
Salt and pepper
Chervil or parsley for garnish, if you like
There are a few general principles that you should keep in mind as you make the soup. First, you don't want to lose any of the starch in the potatoes, because the soup won't thicken as much if the starch is lost. When you cut up potatoes, you'll notice after a few cuts that your knife has a white watery coating on it: that is the starch from the potatoes. If you leave potatoes on your cutting board as you work, their starch will begin to turn your board white as the water that carried it out of the potatoes dries off. For this soup, you want to keep all of that starch in the soup, so you want to place the pieces of potato as you cut them into the liquid you're going to use in the soup.
Second, this is a light-green soup, and you want it to taste "green" and not "brown," where brown here means the savory sweetness that comes from something like browned vegetables or meats cooked over high heat, as on a grill. In addition to the taste, you don't want bits of brown leek or onion floating around in the soup and distracting from its appearance. When you cook the leeks and onions, you want to use low heat so that they won't get browned at all as they get soft and begin to both release and concentrate some of their flavor, which is what you want.
Third, you'll want to use your judgment about what liquid to use to make the soup. I would not use canned stock by itself for this, because the concentrated and somewhat artificial flavor might be too much for the light aromatics (leeks and onions) that you want as the main flavor here. Ideally, you'd use a light chicken stock that you made from leftover chicken bones or some wings or something that you picked up cheaply, but not all of us have that lying around. As a compromise, you might use either plain water, or 2/3 water and 1/3 canned stock, or a bouillon cube or powder in water at a lower concentration (maybe a quarter) of what its package suggests. At school, we used a light chicken stock that we had made; at home when I later made the soup for family and friends, I used about a quart of water and 2-4 tablespoons of a chicken consomme that I happened to have around.
Preparing the Vegetables
Leeks: Using only the white and light green parts, cut the root end off, slice the leek in half lengthwise, and under running water fan the layers a bit like a deck of cards to rinse sand from between the layers. Cut each half crosswise into thin (about 1/8") slices.
Onions: Peel the onion, take the root end off, and cut it crosswise (along lines of latitude) into two or three sections where each section has very roughly the same length (or a bit longer) as the width of a leek (about one to one and a half inches). Slice the onion lengthwise (along what was originally the pole-to-pole orientation of the onion) into slices about 1/8" thick. You want your piles of leeks and onions for the dish to be about the same size, or maybe a bit less onion than leek.
Potatoes: Put about half of the (cold) liquid you're going to use in your soup into a bowl placed next to your cutting board. Peel the potato, and cut it into 4 to 6 pieces lengthwise, like very thick (about 3/4" to 1") french fries. Cut the pieces crosswise into thin chips, about 1/16" thick, and place the chips into the bowl of liquid as you go to keep their starch in what will become your soup.
Melt the butter over medium-low heat in your pot, and add the leeks and onions. Cook them over medium-low heat so that they softly hiss, but never make a popping or snapping sound. This is called "sweating" the vegetables; if they pop or snap, you are "sautéing" them, which will cause them to brown by the time they are cooked, and you don't want that here. You can sweat vegetables at different levels of heat, ranging from low to medium, and the higher the heat you use the more you'll need to shake or stir them to prevent them from beginning to sauté at the edges of the pan. Higher heat takes less time but requires more of your attention.
When the vegetables are soft (after about 5 minutes, though it could be as much as 15 or 20 depending on the level of heat you used), add the liquid with the sliced potatoes. Add additional liquid to cover everything in the pot with room to spare (about 1/2" of liquid on top of the vegetables), and bring it to a simmer, so that it bubbles gently.
You want to cook the soup until the potatoes have released all of their starch into the surrounding liquid, but have not disintegrated. It will probably take about 15 minutes, but could be 10 or 20 or 30 minutes, depending on how thick your potato slices are. You'll see the appearance of the soup change slowly from looking runny, like some vegetables in water where you can see things an inch or more below the surface, to looking more like a hearty soup, with liquid you can't see through anymore. To decide whether to stop cooking, try a bit of potato by plucking it out with a spoon and cooling it for a second in cold water (or just by waiting a minute) and eating it, to see if it could be cooked any more without falling apart.
When the soup is done, season it with salt (a lot, but if you used some canned stock you might already have quite a bit in there) and pepper (white pepper if you have it and don't want to obtrude on the light-green color of the soup).