Well, the cheapest way would be for you to buy a new plug and do some light electrical work (wire stripping and soldering). If it's the phone plug then it's a standard size and you could buy a replacement at Radio Shack (if they're still around). If it's the mic plug you'd have to order it from Spruce or somewhere. Note that this option will not look as good as the factory (but might look okay depending on your level of handiness), but you asked for "least expensive", and this fix could be just a couple of dollars.
If you're not handy with electrical stuff, I imagine any avionics shop could do the same thing for you.
You could probably order a whole replacement cord from Bose.
Of course, you could send it to Bose for repair. If it's under warranty, it will probably be free except the cost of shipping to them. Even if it's not, they might still do it for free. All of the major headset manufacturers seem to be pretty good on free repairs. Plus, they will likely throw in new ear seals, maybe a new head pad, mic muff, etc., while they're at it (they did for me).
Alternately, if you're going to Oshkosh this year and can wait that long, just bring it with you. They will likely fix it right there for free.