Wash and dry the eggplants, then cut the tops off. Slit the flesh in wedge shapes from the top 2-1/2 cm / 1 in down the sides with a sharp knife. Sprinkle with salt and leave upside down on an inclined chopping board for 30 minutes to drain off bitter juices: rinse well.

Meanwhile deseed tomatoes and chop finely. Also finely chop the onion, capers and drained anchovy fillets.

Heat one-third of the oil in a shallow pan, add the onion and cook over a medium heat until golden. Add the drained anchovies and cook until softened. Stir in the tomatoes, capers and chopped basil leaves; season with pepper. Continue cooking until the sauce has thickened. Remove from the heat and add the Pecorino cheese.

Dry the eggplants on paper towels and put them in a pie pan. Fill with the prepared sauce; trickle over the remaining oil and put in a moderate oven (180°C, 350°F) for about 30 minutes.