Preheat oven to 350F (180C). Preheat second frying pan over low heat. Increase heat when ready to sauté the eggplant.
- Lightly sauté the eggplant halves in olive oil in the second frying pan. Start with a little oil (3 tablespoons) but have more at hand since eggplant absorbs a lot of oil and the pan could dry out. This step is simply to soften the eggplant a bit, so sauté quickly on both sides, remove, and drain on a rack (do not wipe off the oil).
- Place the eggplant halves on the bottom of a baking or roasting pan. Sprinkle some of the cheese to cover the bottom of the well in the eggplant, then spoon in the filling to the top of the side rims.
- Spoon over the béchamel sauce (about 1 tablespoon for each piece), and place a slice of tomato on top.
- When all the eggplants are finished, sprinkle the remaining grated cheese over the top.
- Cook on the lowest oven rack setting until the béchamel is browned, the cheese on top is browned, and the eggplants are soft, 1 to 1 1/2 hours.
We got the idea of sprinkling the well of the eggplant with grated cheese before filling from a recipe by Diane Kochilas, one of the great Greek cooks and author of some of the finest Greek food cookbooks in print.