Step 1: Reuse
Hack the broken cord off with scissors, or a giant machete, or whatever you have handy about 4" from the base of the cord.
Then, go to your local Transistor Hut, and pick up a new headphone jack. (~$4), some solder (~$3) and a soldering iron ($? I had one already).
Use a pair of wire strippers, or a knife (giant machetes unwieldy for this step), strip the outer housing, and the three (in my case) wires on the inside.
These particular headphones had a red wire, a white wire and a yellow wire.
Step 2: Solder
The weird thing is, it sounded alright, but biased to the left ear. Even weirder (to me), the right ear sounded pretty good except that the vocals were garbled. Instruments, for the most part, sounded fine.
Anyway - I found some other references for wiring up these little jacks, and it seemed like a lot of headphones have two ground wires, but they all seemed to have red and yellow wires as well. So, I figured white must be ground, switched the wires, and voila, everything sounds fine.
I might have gotten left and right reversed, but I haven't been able to tell yet. Can't find a song where I know something's supposed to be on a particular side.
One thing to remember: BEFORE you solder the wires to the jack, remember to slide the stress reliever, exterior housing, and the little plastic sheath over the wire. If you solder, then remember to do this stuff, you're screwed. (no, I remembered at the last second. Lucky me.)
Step 3: Finishing Up
I should point out that yes, I know this project's ludicrously simple. No, it's not going to change the world. No, most people aren't going to have a pair of AKG's lying around whose cord they've ruined by careless office chair-rolling.
That said, it's surprising how useful this new setup is at my work, and how nice it is not to constantly be watching out for cords. I can get up, turn around, sit back down and not have to untangle myself, and I don't get that irritating hiss that most wireless headphones seem to be cursed with.
Step 4: Plug In, Rock Out
Unfortunately, the volume control's upside down, but that's not really that big a deal. If you're really desperate to mount it right-side up, hope that you have a longer piece of cord to work with.
While this project unfortunately isn't terribly practical unless you happen to have wrecked the cord on a relatively large pair of headphones, if you *have* happened to do such a thing, it'll bring an old, ruined pair of headphones back to life.
Better still, if I want to use the headphones in a more traditional way, I can just plug them in to a headphone extension cord and presto, old-skool functionality restored.