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Cut the eggplants into 7mm round slices (you will have about 44 slices). Put them into a large bowl or colander, sprinkle with a tablespoon of coarse salt and leave to drain for 30 minutes or longer. Rinse, then lay them onto tea towels to dry. Put the flour in a shallow bowl and pat the eggplants on both sides to coat, shaking away the excess.
Line a couple of large plates with paper towels. Put enough oil in a large frying pan to go about 3 cm up the sides. Fry the slices in batches over a medium-high heat until nicely golden on both sides. As the slices are done, hold them up with tongs over the pan to drip excess oil back in. Put them on the plates to absorb oil and sprinkle lightly with salt.
While the eggplants are frying, make your tomato salsa. Heat the olive oil in a wide pot with the garlic. When it starts to smell good, add the tomato. Swish out the bottle with 250ml of hot water and add this to the pot. Season with 1 teaspoon of salt and a couple of grinds of pepper, and simmer for about 15 minutes or until thickened, putting a lid on to partly cover if it is splashing. Tear in the basil leaves and cook for a couple of minutes more, then remove from the heat.
Meanwhile, preheat the oven to 190°C. Put the mozzarella onto a plate and the parmesan onto another. Use a spoon to roughly divide each of them into 4.
Remove the garlic from the sauce, then dollop about 125ml of it onto the bottom of a 22cm x 30cm oven dish. Cover with a quarter of the eggplant slices in a layer (10-12 slices), then scatter over a quarter of the mozzarella, followed by a quarter of the parmesan. Repeat the layering 3 more times, finishing with the scattering of parmesan. (On the final layer you will probably have more sauce – use it all here.)
Put into the hot oven until golden and a bit crusty here and there, for about 30 minutes. Remove and let cool slightly. Cut into good squares, scatter with basil leaves and serve warm. It is also good the next day.