Ingredients
1 UTP Ethernet cable, old (possibly broken, this one had a single wire broken at a connector).
1 roll of aluminium foil.
1 mini (3.5mm) headphone plug (could - and perhaps should - be replaced with either a Canare "barrel" plug or a full-size stereo plug).
Lots of copper wire for an additional interference screen.
Thread.
Some kind of isolation coat once the cable's done.
Tools
Soldering iron and solder.
Pliers, the smaller and finer the better.
Sharp scissors or nailcutter.
Sharp, small knife.
Lighter or candle.
The first step is skinning of the UTP cable. The sharper the knife's point, the better (maybe a scalpel could do too). PVC skin is picked up/cut from within the cable, a long straight cut usually allows skin to be ripped apart by hands.
Second is braiding of the wires; wires inside a UTP cable are already twisted in pairs, but they're often not twisted together. Star quad cable has four conductors per channel, so two twisted pairs should be braided together at the same twisting length as the original twist.
Here's the wire arrangement inside a star-quad cable: negative pair perpendicular to positive pair.

Third, each twisted pair's wire ends have to be woven together. So one pair becomes the negative, and another the positive conductor. This is the idea behind star-quad cable: each conductor (negative/positive) is duplicated over a twisted pair to minimise sensitivity to interference, and the two pairs are combined together to absorb any phase interference. Hence star-quad is noticeably more clean even with an unbalanced connection. The copper wires can be a tad too fragile, skinning the isolation coat off them can clip the wires; but it can be burned with a lighter or a candle. For the sake of termination, only a couple millimetres are best exposed, otherwise wires can short once connected to the plug.
Fourth, the termination. A miniplug will do, but a miniplug can be a bit too small for the double conductors, hence a Canare "barrel" plug or a full-size stereo plug might be a better choice. For a miniplug connection, different conductor wires have to be carefully arranged in such a way as to not touch one another. A miniplug on the inside has the top sleeve connecting to common negative/ground, right (top) connector for left channel, and left (bottom) connector for right; same as the plug conductor layout.

The two negative double conductors are connected to miniplug top sleeve, and the left/right channel double-conductors to their respective terminals inside the miniplug. Wires can be thrown onto a working headphone set's 3.5mm plug for testing.
Once everything's confirmed working and there are no shorting wires, the wires inside the miniplug can be soldered. After soldering, the miniplug's usually filled with epoxy resin or plastiline, to ensure soldered wires won't move.
Note: make sure the miniplug cover and strain relief are placed on the cable before the next step, and the cable works properly with the cover screwed on. If it doesn't, check the wires for shorting. Regular 3.5mm plugs don't have much space inside, wires can short unless isolated properly (even with wire ends exposed, a bit of insulating plastic or masking tape can help). A full-size headphone plug or a Canare "fat barrel" 3.5mm plug are easier to work with, but they're more cumbersome and will place more stress on a minijack of a portable player or amp.
Once the cable is confirmed working (by throwing the wires on headphones' diaphragm terminals or miniplug), it can be dressed in aluminium foil. Several strands of aluminium foil will be required, and it can be held together with tied thread.


For additional resistance to interference, the cable can be enclosed in another layer of copper wire, wrapped around the aluminium foil. The final touch is a coat of isolation/PVC. Transparent isolation will make the cable look especially pretty :=) .
The last step is desoldering old wires and soldering diaphragm terminals to the new cable. If the terminals aren't clearly marked as negative/positive (they aren't on the K-81), phase can be checked with a low-frequency pulse tone: the diaphragm will lift if it is connected correctly, and drop to the magnet if it isn't. Here's a tone that works for the purpose:
http://www.headphonedeals.org/Audiotest/46 Square Wave Grind.flac.