Set your oven to warm at 200C.
Using your kitchen knife slice the eggplants in about 1cm slices. I like mine sliced across the width, but others ask for slices along the length if you are using long fruit.
Line the baking tray with baking paper. You can do without, but your slices will stick to the baking tray and be a tad difficult to get off the pan whole.
Lay the slices of eggplant on the baking tray and drizzle oil over them. If you are just using a baking tray oil the surface of the tray before putting the eggplant slices on it.
Pop eggplant into the oven. They will take between 45 mins to 1 hour to soften and brown. Check at 30 minutes just in case.
Meanwhile, pour 250 g of the pasta sauce/sugo into the saucepan. Heat till a good simmer.
Add either the cherry tomatoes or diced ordinary tomatoes.
Meanwhile, grate the parmesan and mozzarella.
As the cherry or ordinary tomatoes cook, they should begin collapsing. You can help this along with a potato masher.
Add a pinch of salt and of pepper also to the sauce.
Keep simmering the sauce till it is quite thick.
Check on your eggplant and when they are soft and brown they are ready to use.
Line the casserole dish with olive oil.
Put in a single layer of the eggplant to cover the base of the casserole dish.
Spoon over a third of the pasta sauce. Make sure all of the eggplant is covered - you may have to spread it thin - that's alright.
Place a third of the basil leaves on top of the sauced eggplant.
Sprinkle a third of each of the cheeses on top of the sauce right to the edge of the casserole dish.
Do all of this with the eggplant, sauce, cheese and basil leaves again.
Do all this a third time finishing with the cheeses on the top of the dish.
Put the parmigiana into the oven. It will take between 1/2 and 3/4 of an hour for the parmigiana to cook - you want the cheese brown and melted and there will be some sauce bubbling up the sides of the casserole dish also. Check after 30 mins just in case.
When it's ready put more basil leaves on top of the dish.
Serve.