Cut eggplant slices about 1/2 inch thick. If you are cooking in a baking dish, cutting the eggplant lengthwise may work better, otherwise you can cut horizontally like I have done.
Place eggplant slices in a colander, salt and let the eggplant sit for about an hour, this helps remove the bitterness. If you are using the white Santorini, you can skip this step.
Preheat oven at 450 degrees Fahrenheit (230 Celsius), if baking eggplant. If you are sautéing eggplant then just preheat oven at 350 Fahrenheit (180 Celsius).
Prepare sauce by sautéing onion until translucent in 2 teaspoons olive oil. Add garlic continue sautéing for another minute.
Add the tomatoes and simmer for about 15-20 minutes.
Now either lightly saute the slices in olive oil placing them on napkins, or bake in preheated oven of 450 degrees Fahrenheit (230 Celsius). To bake, brush a pan with olive oil, toss the eggplant slices in olive oil and bake for 15-20 minutes.
Once your eggplant slices have been sautéed or baked begin assembling. Lower oven temperature to 350 degrees Fahrenheit (180 Celsius).
Brush a pan with olive oil or you can spread tomato sauce, place the eggplant, then tomato sauce, then basil and then cheese, repeat this until you have finished with a layer of cheese. It is kind of like putting together lasagna. I also added a few drops of olive oil between layers.
Bake in the oven for about 30 minutes, until eggplant is soft.
Serve.