Wash the aubergines and cut them into slices 1 cm thick; put them in a colander, in layers, and sprinkle a little coarse salt on each layer. Place a plate on top and leave for about half an hour to extract the bitter water they contain. Then rinse the slices, one by one, and pat them dry with a cloth or kitchen paper. Dip them in the flour, then shake lightly to eliminate any excess and fry them in plenty of hot olive oil. When they’re golden brown on both sides, remove them from the oil and place them on absorbent kitchen paper to dry. Lay the slices, one beside the other, on a baking tray lined with greaseproof paper. Thinly slice the tomatoes, cut 10 of the basil leaves into thin strips and put them both into a bowl with the chilli pepper. Mix them together and put a spoonful on top of each slice of aubergine; season with salt and a sprinkling of grated pecorino. Bake in a preheated oven, at 200 °C, for 10 minutes.
Before serving, garnish each slice with the remaining basil leaves.