Slice the eggplants into 1cm thick rounds, and set them aside. Whether you are using a cast-iron pan or a barbecue, it needs to be very hot. Meanwhile, put 2 or 3 tablespoons of olive oil into a large saucepan over a medium heat. Add the onion, garlic, and dried oregano, and cook for 10 minutes, until the onion is tender and the garlic has a little bit of colour. For canned tomatoes, chop them up, and for fresh tomatoes, quickly prick each one and put them into a large pot of boiling water for 40 seconds. Remove with a slotted spoon and put into a bowl of cold water for 30 seconds, then remove the skins, carefully remove the seeds, and chop the flesh. Add the tomato flesh or canned tomatoes to the onion, garlic, and oregano. Give the mixture a good stir, then put a lid on the saucepan and let it simmer gently for 15 minutes.

Meanwhile, grill the eggplant slices on both sides until they are slightly charred – do them in batches. When one batch is done, transfer them to a plate and continue grilling the rest until they are all ready. When the tomato sauce has reduced, season carefully with salt, pepper, and a little wine vinegar, and add the basil. There can be chunks in the sauce or it can be reduced to a puree.

Take a terracotta dish (25 x 12-15cm). Put a small layer of tomato sauce, then a thin layer of Parmesan, followed by a single layer of eggplant. Repeat these layers until all the ingredients have been used, finishing with a little sauce and Parmesan. You can mix the breadcrumbs with olive oil, a little chopped fresh oregano, and put on top of the Parmesan. Sometimes the dish is served with mozzarella on top, which is also good.

Put the dish in the oven and cook at 190°C/375°F/gas 5 for 30 minutes, until golden, lively, and bubbling. It is best to eat the dish immediately, but it can also be served cold.