Warning! High voltage transformers are extremely dangerous, even more so than most Tesla coils. They put out considerable amounts of 60 Hz power at voltages that look at human flesh as a short circuit. This transformer, unlike a pole pig, won't set you on fire, since it has a built-in current regulator. It will, however, put you into cardiac arrest and give you severe burns. Don't mess with it! If you haven't read the warning and legal shit at the bottom, do so.

Note: this design is untested.

I haven't digitized the schematic for this transformer yet, but here are the directions:

1. Get hold of:
    500 feet of either 10 AWG uninsulated wire, 1/8" aircraft cable (that's what I'm using, for cost reasons), or something similar
    2 15" long, 1" diameter steel rods (call your local iron store)
    800 feet of 32 AWG wire
    2 suitable, watertight enclosures for the two cores and some windings, which will be about 3" diameter total
    Enough oil (preferably transformer oil, but motor oil will *probably* work) to fill your two enclosures
    If your enclosures don't have them, lugs for the transformer's output
    Varnish, or some other paintable insulator
2. Now it's time to start winding. Pick one of the cores to be your low voltage core. Now, wind the 10 AWG or whatever you picked for the thick wire from one-half inch from the end of this core until you get 20 turns, painting your insulator all over. When this is done, make the end of the 20th turn stick where it is by whatever means you like (it should be a permanent job), and take it back to the beginning of the coil. Repeat the winging and returning to the beginning 4 more times, using a different spot for the return every time.
    I've seen a suggestion to get a good movie or two for while you do this, and I recommend it unless you have an amazingly low IQ, because winding many, many turns is astoundingly boring. Wind 1000 turns of the 32 AWG on the coil form (you don't have to layer this or any of the other two you'll be doing), starting about half an inch from the winding you just finished. Connect both windings to their lugs and fill the transformer with oil. You've just built a working transformer! If you just wanted 2400 VAC at 1.5 amps, you could stop here. We're building a 24 kV transformer, though, so go on to the next section.
3. Take your other core, get a few more good movies, and sit down on your couch again. Now you have to do one winding of 100 turns and one of 1000 on this core, which should be spaced about an inch apart. Now connect these windings to their lugs and fill the transformer with oil.
4. Connect the primary of the high-voltage transformer to the secondary of the low-voltage transformer. Congratulations--you're done!