Top & tail the okra, then slice it in half vertically.
Do the same to the eggplant. Make the slices about 1/4" thick.
Lay out the okra slices on a plate to air-dry.
Brush both sides of all the eggplant slices with liberally with salt. Leave them for at least an hour to release moisture.
Dry off the eggplant slices and remove all visible salt.
Spray both sides of the okra and eggplant slices with oil, then place them on a shallow baking tray lined with baking paper.
Bake in a moderate oven until lightly roasted. This should take about 30 minutes.
Meanwhile, make the sauce. Heat the oil in a frying pan over low-moderate heat then add the onion and tomatoes. Cook gently and slowly, gradually reducing and increasing the sauce by adding small amounts of water here and there. Keep an eye on it and stir continually so it doesn't catch.
Once the tomato pulp has separated from the skins, remove the skins from the sauce. Continue cooking the sauce until all the ingredients are well cooked and blended- you want it liquid enough to be a sauce, but not runny and watery. It should take 1.5-2 hours to make the sauce.
Prepare the meal for baking. Using a deep baking dish, layer the sauce then vegetables then cheeses (and basil, if using) over and over again until all your ingredients have been used.
Bake on 180C (355F) for 25 minutes.