While this isn't a definitive answer, I've given it some further thought and believe that my original suspicion is probably correct. That is, the saltiness is probably due to the chicken itself, and the kashrut is a likely root cause.
For the benefit of anyone unfamiliar with the koshering process for poultry, in a nutshell it involves removing the feathers and various other parts, then thoroughly coating it in koshering salt, which are flat, coarse-grained crystals that are ideal for sticking to the meat (unlike table salt crystals which would dissolve, or sea salt crystals which would just fall off).
The koshering process desiccates (dries out) the meat - the salt crystals absorb moisture, and then they are washed off, taking the moisture with them. It's mainly done to remove the blood, but at the same time removes a lot of other moisture. The entire process only takes about an hour and does not add a significant quantity of salt to the meat. Kosher salt crystals can absorb quite a bit of water before they dissolve and without being in a solution, they cannot actually penetrate the meat.
This is in contrast to brining, where the chicken is immersed in a saline solution and actually absorbs up to 10% of its weight in brine (which adds up to about 0.05% of its weight in salt for a typical solution of 5% brine). This actually does makes the chicken saltier throughout, although very few people actually perceive this as "salty" - it just enhances the flavour of the chicken.
So if a brined chicken, which has actually absorbed salt, doesn't taste particularly salty, then a kosher chicken should definitely not taste salty, and normally it won't. The caveat is that this assumes that the plant was diligent in its preparation of the chicken before packaging, and depending on where you live, many if not most kosher factories are anything but.
Specifically, there are a few ways a kosher processing plant could, by virtue of carelessness, produce chicken or other meat that's way too salty:
- They can apply far too much salt to begin with;
- They can salt it for too long;
- They can wash it poorly or not at all.
All of these factors will compound each other leading to roughly the same effects:
- The meat may become noticeably dry;
- Crystals of salt may be deposited on the exterior, undissolved;
- Over time some of those crystals may actually absorb enough water to dissolve, creating its own "brine" of sorts and even diffusing the super-saturated salt-water back into the meat. Koshering is a time-sensitive process.
If you're also noticing any dryness in the meat then I would definitely think they were being less-than-thorough at the factory and suggest looking into different brands or even filing a complaint.
Even if that's not the case, or if you don't have that option, one thing you can probably do at home to compensate is to simply rinse the chicken thoroughly before cooking it. Note that this is not for food safety, and rinsing a chicken is known to actually raise your risk (slightly) due to cross-contamination concerns. But you are not doing this for food safety, you are doing this to get rid of non-bacterial contaminants (salt, and maybe other things) that the factory left behind.
Undissolved salt on the surface is definitely going to taste the saltiest since you'll be putting actual whole crystals on your tongue, and I think that's a very likely culprit here. Salt and other solids really have a hard time penetrating the exterior of meat or poultry, so it's less likely for the salt to be inside the chicken, even if the processing plant was truly sloppy.
So try giving those kosher chickens a good rinse - don't forget to sanitize your work area when you're all done preparing them - and see if that helps you at all. If not, then probably all you can do is find another brand or try to mask the saltiness with a lot of spices and sauce (find a recipe that's normally heavy on salt, and cut the quantity of salt used).
P.S. Note that this is quite speculative and I do not actually have first-hand evidence of this happening at a kosher factory. Nevertheless, it is the best explanation I can think of for a kosher chicken coming out too salty when there is no salt at all in the recipe. I've never had it happen with an unkosher chicken.
Speaking as pure theorist here, because I've never compared the saltiness of cooked chicken.
I think that there are two things you will have to think about. The first one is osmosis (water that gets soaked into the meat through cellular membranes), the second one is transport through porous media - like a sponge, the open ends of muscle fibres of your chicken soak up the liquid you put them in. What you want to do is to prevent osmosis into the chicken (because only pure water will go in through osmosis, concentrating the salt outside) and maximize absorption. I will assume that 0.9% saline is isotonic for a chicken, and I think this is a safe assumption, because veterinary saline isn't marked as species-specific. Seeing that your soup liquid is 0.27% saline, you can expect some osmosis to happen. *
Let's tackle the more interesting part first. You want more absorption to happen. The absorption is described by the Washburn formula,
and you want to maximize your L.
L improves with time. Luckily, a soup is meant to be cooked for a long time anyway. But when you wonder whether to give it some more time on the stove or not, more time is probably better. Keep the temperature lowish for less evaporation, and a lid on which will drip back evaporated water.
L improves with lesser viscosity. No way to influence it in your basic recipe, but in a real soup, avoid thickening. So don't use starchy ingredients, or at least, wash them before adding.
Surface tension should be kept high. Again, this is ingredient-specific. No way to influence it in the basic recipe, but it could turn out that some vegetables are reducing your surface tension a lot - I can't think of a soup vegetable or a herb or spice which is famous for a high saponine content, but it could happen. Also, you should give your pots a finishing wash with clean water if possible - detergent and dishwasher finishing liquid reduce surface tension a lot.
Pore size. My intuition says that this should have the biggest effect in the soup case, as you probably can't influence viscosity and surface tension too much. Obviously, the bigger your holes, the more water comes through. A good way to do that is to thoroughly denature your proteins. The first and most common way for that is prolonged cooking time. Second, brining in concentrated saline (6%) and/or acid before you cook will attack the meat surface, again denaturing proteins. However, I don't know how wise it is to use this option, because some of the brine will get absorbed into the chicken, which will leave less space for broth and will increase salt content as a whole. (This assumes that you salt the broth; Brian's idea of not adding salt to the cooking water after brining has merit). Third, you can use meat from the freezer (this is a very likely reason for the mixed results you saw until now). Freezing produces ice crystals, which rupture cell walls. When you use the thawed meat in a soup, there are more holes for water to flow in.
The Washburn formula is for a single capillary. But the more capillaries you have, the more absorption you get. So, what you want to do is to cut the chicken meat perpendicularly to the muscle fibres. And cut it into many small pieces instead of a few big ones.
Now we took care of the absorption, let's look into the osmosis. You can't change the salt content of the chicken's cytoplasm. But for osmosis, you have to separate the two solutions by a semipermeable membrane (the cell wall). Poke a hole in the wall, and the osmotic gradient vanishes when the liquids mix. So everything from the third point on absorption helps you reduce osmosis too.
As for your suggestions: 1. I see no reason why slow or quick heating will change absorption. I guess the products of a Maillard reaction could clog some pores, if you sear before cooking, but it won't happen during boiling. As I said, cook slow because of evaporation. 2. The chicken shouldn't absorb salt, but salty water, see the footnote. Although, if there is a hole in my theory, this is a likely place for it. 3. I doubt it, but if you wash it, you could free eventual clogged openings. 4. Certainly, cook longer.
To summarize: Cook meat which has been frozen, cut in small pieces perpendicularly to the grain, and stew it for a long time.
* I don't see a mechanism for the chicken absorbing a higher percentage of salt than what you have in the broth. I assume that in your "normal" cases, you are left with salt content near the initial 0.27%, and in bad cases, this gets concentrated.
Update As requested in the comments, I am providing an explanation about "cutting across the fibers". Short story, meat is made up of muscles, and a muscle is made up of fibers, or bundles of bundles of cells. You can easily see them in raw meat. You want to slice across them, so their ends are open, as opposed to along.
The good, long explanation with pictures can be found on Serious Eats
Best Answer
Does it work? Yes, it does.
The idea is to create something akin to an individual "dutch oven" around the chicken or fish you are baking. The meat is "steamed" in his own juices. There are a bunch of different "recipes" for the salt crust, often with some "binding agent" like egg whites. Usually, the skin is removed when serving (go ahead, give it a try, if you like), so rest assured that the meat underneath is not too salty.
An alternative to salt (and arguably more "paleo style") would be baking in clay.
A quick internet search should yield plenty of recipes for both varieties.
(Remenber: asking for recipes is a big no-no here.)