Too many chicken soup recipes (and a shocking number of chicken stock recipes) call for simmering raw chicken in water to produce the soup base. Adding to the confusion is a hazy understanding of the difference between broth and stock and a tendency among recipe writers to conflate these terms. We'll get to that in a moment, but for starters, all you need to know is that stock is made from simmering bones, while broth is made from simmering meat.
Now, there are all sorts of problems with simmering raw chicken, not least being the fact it causes a protein called myoglobin to ooze out, which, along with other impurities, forms a layer of (there's no better word for it) scum, which rises to the surface.
You can stand there and skim this scum or not, but it will make your soup cloudy if you don't. Conversely, standing there skimming it is not a good use of your time.
Make the Stock Separately
The answer is to make your stock first and then add additional ingredients—like chicken, vegetables, and noodles—separately in order to transform the stock to your chicken soup.
The beauty of this technique is that making the soup itself is extremely quick. The main thing you're waiting for is for the vegetables to cook. Carrots take the longest, but 15 minutes should do it.
Go the Homemade Stock Route
Making chicken stock used to be a fairly involved process (though not so involved as making brown stocks), but that was before the Instant Pot. Not since fire itself has any innovation so transformed any area of the culinary arts the way the Instant Pot has revolutionized stock-making.
You simply add chicken feet to the pot, along with water, aromatic vegetables (i.e. carrots, celery, and onions), and a few seasonings, like whole black peppercorns and a bay leaf. Then, turn it on to the "bone broth" setting and walk away. When the timer goes off, release the steam, strain, and either chill for later or proceed to make your soup.
You can usually find chicken feet at Asian grocery stores. They're loaded with chicken flavor, and they're practically pure cartilage, which when simmered, breaks down into gelatin, which is what makes the finished stock jell in the fridge. Chicken feet are the single best ingredient for making chicken stock.
Use a Flavorful Stock
The primary source of flavor in the soup should be the broth or stock, not the chicken or other ingredients. Sure, chicken meat has a certain amount of flavor. Dark meat has more and white meat has less, and the bones and fat have some as well. But whatever flavor that chicken has, once you add it to the soup, you're merely redistributing that flavor, but you're not concentrating it or making that chicken more flavorful than it was. Truth be told, all you've done is make that chicken flavor weaker by diluting it with water.
Don't Swap In Broth
There is, indeed, a very good reason for distinguishing between broth and stock. As we mentioned earlier, stock is made from simmering bones, while broth is made from simmering meat. And lest you think this is mere semantics, consider that which gives stock its body (i.e. the quality that causes it to jell when you chill it) is the fact that simmering bones slowly for a long time dissolves the cartilage at the joints of the bones and turns it into gelatin.
But it takes time for this to happen. Simmering meat for that long only turns it stringy and overcooked. You'll extract flavor from it, but you'll be ruining the meat itself. This is neither a good use of your time nor your money.
So, stock is stock and broth is broth. For maximum flavor and body in your soup, you need the former. And despite the myriad products labeled "chicken stock" on the supermarket shelves, the best chicken stock is one you make yourself.
Add Chicken Feet
Yes, you read that right: chicken feet. If you want to make a truly exceptional chicken soup, don't bother simmering a chicken carcass, bones, meat, or anything like that. Simply head to your Asian grocery store and pick up a pound of chicken feet, which is enough for about four quarts of insanely flavorful chicken stock.
Chicken feet are unusual-looking for sure, but they're loaded with cartilage, which will impart marvelous body to your stock. Plus, they pack a ton of rich chicken flavor. Along with using the Instant Pot, chicken feet might be the single best tip for upgrading your chicken stock, and thus your chicken soup.
Season With Kosher Salt
Conventional wisdom says that you shouldn't season your chicken stock, because if you're using that stock to make a sauce, you'll reduce it and concentrate the saltiness. Which is true as far as it goes. But if you know you're making chicken soup, you might as well go ahead and add a teaspoon of Kosher salt for every three cups of water you add to the Instant Pot.
You can also skip this and season the soup–with the difference being that the seasonings won't penetrate the meat and noodles quite as much as if they were in there from the start–but it's certainly a conservative approach and it'll work fine. The point, though, is to be sure to season your soup.
Add Noodles Toward the End of Cooking
Other than the carrots, the only thing that takes any time at all are the noodles. Simply check the cooking time on the package of noodles or pasta you're using and add them to the soup that many minutes before you're ready to serve.
Cooked Chicken Meat Goes In Last
For a deeply flavorful chicken soup, get some boneless, skinless chicken thighs, season them, brown them in a skillet, then finish them in a 375 F oven. You can refrigerate them until you're ready to make the soup, then simply dice them up and add them to the soup at the very end. You're not cooking this meat in the soup; you're just warming it up. It shouldn't take more than a minute or two.
Then, simply check the seasoning, adjust as necessary, and serve.