1. Preheat the oven to 350°F.

2. Set a large skillet over medium heat and pour in 1/2 cup olive oil. When the oil is warm, after  about a minute or so, add half of the diced eggplant. (You want to shallow-fry the eggplant in batches, so you don’t overcrowd the pan; otherwise, the eggplant will end up steaming or braising, which would result in less flavor and a mushier texture. Of course, if you have two large pans, you can cook both batches at once.)

3. Cook the eggplant, stirring frequently with a wooden spoon, until you get some nice color and crispness, about 7 minutes.

4. Add 1 clove garlic and cook for another minute, then add half the onion and cook for another 3 minutes or so, until the onion gets some caramelization too.

5. Add half the tomatoes to the pan and cook, stirring now and then and breaking up the tomatoes with the wooden spoon, until a light sauce forms, about 10 minutes.

6. Season the eggplant mixture with salt and pepper and add 1 basil leaf to the pan. Give everything a quick stir, then transfer to an 8-inch square baking dish and set aside.  Repeat with the remaining 1/2 cup oil, eggplant, garlic, onions, tomatoes, salt, pepper, and basil. Add to the baking dish and stir to combine.

7. Pop the dish, uncovered, into the oven and bake for about 10 minutes, until the eggplant is soft but not too soft—you still want some texture there.

8. Scatter the Parmigiano over the eggplant and bake for another 3 to 4 minutes, until the cheese is golden and bubbling.

9. Remove the dish from the oven and let cool to your preferred temperature. You can eat this hot, at room temperature, or cold.