A lot of people never cook eggplant. It’s a shame, because eggplant are easy and delicious.
Most eggplant recipes include directions for salting to “draw out bitterness.” This step has always mystified me, and perhaps it’s a relic of some long ago time when eggplant were actually bitter. But I’ve eaten literally hundreds of eggplant and never tasted anything bitter. So skip the salting.
Most of the writing about eggplant also claims that it soaks up a lot of oil. It will if you let it, but you don’t need that much to cook it.
You do need a cast iron skillet, although other heavy pans might work as well. However, if you don’t have a cast iron skillet, go out and buy one. I have more than a dozen cast iron skillets in my kitchen and I use at least one or two every day. Vintage pans from Griswold are the best, but brand new Lodge skillets are fine and cheap. I wouldn’t pay extra for the pre-seasoned pans, but that’s your call (the myths about cast iron seasoning are rampant; here’s how I use and take care of mine).
For the typical globe eggplant, slice the ends off, cut the eggplant into round slices about a half-inch thick, then cut those into roughly square cubes. Put your cast iron skillet over a medium high flame and let it heat up for a few minutes, then pour in enough extra virgin olive oil to just cover the bottom of the pan. Wait a minute or so for the oil to get hot, then add the eggplant and let it sit without stirring for at least a couple of minutes. When the cubes start to brown just a bit, use a stiff spatula to scrape and turn them.
Continue cooking, adjusting the heat if necessary and turning occasionally, until the eggplant is nicely browned. This usually takes less than 10 minutes. Depending on what you’re making, you can add other ingredients to the same skillet or set the eggplant aside for adding later.