Here's the ingredients: One eggplant, some dashi (light Japanese-style soup stock), soy sauce, sugar and mirin (cooking sake).
Cut away the stalk and slice the eggplant lengthwise. Make shallow crosswise cuts in the skin side of each half, about a centimeter apart. Be careful not to cut too deep.
Fry up the eggplant quickly on both sides. You don't want to cook it, but just brown the surface a bit. It adds to the flavour and it makes the eggplant hold together better.
Prepare the dashi and boil it up. You'll want around 20cl or so. Put the eggplants cut side down in a small pot just big enough to hold them. Pour over the hot dashi. Not too much; you want the top half of the eggplant uncovered. Then add about 1 teaspoon sugar, and 1 tablespoon each of mirin and soy sauce. You want the stock to be flavourful but not thick. Bring it up to a slow boil.
Simmer the eggplants for about five-ten minutes or so. Turn them over a couple of times - be careful; they're soft - so both sides get to simmer and soak in the liquid. They're done when they're really soft and the stock has reduced a bit. Turn off the heat and let them cool down under a lid.