Brining a kosher bird

I'll try to weigh on in this as much as possible with a non-authoritative answer:

First of all, I simply can't state this emphatically enough: kashering is not brining! A kosher bird is not "pre-brined", and professional chefs who claim that it is are either misinforming their audiences or simply misinformed themselves.

Kashering (sometimes called koshering) has the principal aim of drawing blood out of the meat. This page explains the process but to summarize: first the unkosher parts are removed (feathers, blood vessels, etc.), then it is soaked without salt for 30 minutes, then it is coated in kosher salt (AKA kashering salt) and left to rest for 1 hour, and then finally it is thoroughly washed again to remove the salt crystals (in theory, anyway - sometimes the salt is not thoroughly washed off).

This could not possibly be more different from brining! In the kashering process, moisture is drawn out and the meat generally ends up tougher. This is especially noticeable with red meats as opposed to birds; ask anybody who's ever tried to cook a moderately-priced kosher steak from the supermarket and they will likely tell you without a hint of irony that not even a strong acid marinade, several minutes with a mallet and several hours in the crock pot can turn it into anything other than shoe leather.

But I digress. Brining is a long, slow, steady process which adds moisture to the meat. Its aim is both to add flavour and to tenderize. According to McGee, brining increases the weight of the bird by 10% or more; of course, moisture is still lost during the cooking process, but the same amount of moisture is lost whether it is brined or not, so a brined bird will be 10% more moist after cooking.

Kashering is roughly equivalent to "dry brining" when the meat is simply coated in salt. In my opinion this "dry brining" has absolutely no business being called a "brine" at all, which is defined as:

a : water saturated or strongly impregnated with common salt
b : a strong saline solution (as of calcium chloride)

Proponents of this method argue that it's technically a brine because once it starts to draw out moisture from the bird then it creates a solution (brine). While not wanting to sound overly nit-picky, I think it's very obvious that when people talk about "brining" a bird in the traditional sense, that isn't what they mean. It's a vastly different method that produces a vastly different result - imparting a different flavour and leading to a very different texture.

I'm sorry to have dwelled on this point for so long, but I think that background is necessary to really understand the question. Kosher birds may come out with a similar flavour to non-kosher brined birds in the absence of any other preparation - emphasis on similar because no sugar is involved in kashering - but brining a bird is not simply about adding salt, it's about adding brine. Brine, by definition, includes water.

So what do you do if you have a bird that's already been salted but not actually brined, and you want to achieve a result that's somewhere in the vicinity of a real brining?

Add water.

That's really the only missing ingredient here - that and sugar, if you like to use that in your brine. You've already got the salt. You might want to add some salt as well because kashering does not increase the salinity of the bird as much as brining due to the extremely short exposure. Exactly how salty the kosher bird will be is anyone's guess, because it depends on the exact amount (and consistency) of salt that was added during the kashering process, how long it was left to rest, and how thoroughly it was washed afterward. A traditional process like kashering doesn't lend itself well to automation which means there is going to be a lot of inconsistency from distributor to distributor and even from bird to bird.

My best suggestion would be to err on the side of caution. A kosher bird doesn't need to be brined for flavour - that point is not in dispute. I've seen "rules of thumb" that suggests using half as much salt and brining for half as long. I think that's a good starting point, but if you know for a fact that the kosher birds you buy are already fairly salty (in the sense that you could roast one straight out of the package and never need to reach for the salt shaker) then use less - say 1/4 of the amount that you would normally use. But don't reduce the sugar, because the kosher bird definitely hasn't been exposed to any; and additionally, a generous amount of sugar in the brine will help to prevent the weaker brine from drawing salt out of the bird.

But all told, it's way easier to add salt to a slightly bland bird than it is to try to save an over-salted bird. So use as little salt as possible if you plan to brine a kosher bird, at least for your first attempt. Again, my rule of thumb would be 25% of the normal salt and 100% of the normal sugar, and follow the usual advice to brine for only 50% of the usual time. If you find that it comes out a little bland, then next time you can let it brine for a little longer or increase the salt to as much as 50% of normal.

50% salinity should probably be your upper limit; kashering (or dry-brining), despite its shorter duration, tends to incorporate a good deal more salt, proportional to the time. As per the link that Jefromi posted, some people claim that the salinity of a kosher bird is already approximately equal to that of a brined bird; another 15-25% increase won't make a huge difference but another 30-50% almost certainly will - and not in a good way.

If you want to be really scientific about this, get yourself a salinity meter such as this one, start with a mild brine, and measure both its volume and its exact salinity before and after the brining process. That will tell you without bias exactly how much additional salt is actually being added to (or removed from) the bird. Obviously I don't have time to do this experiment myself right now, but if anyone owns a salinity meter and wants to try this out, feel free to report the results and I'll do the number crunching and edit this answer with the findings.