Wash the aubergines and cut in half lengthways. Arrange on a rack, sprinkle with salt and leave for half an hour. Then wash off any remaining salt and pat dry with kitchen paper.
Gently fry the cloves of garlic in a frying pan with a dash of extra-virgin olive oil and remove once they have turned golden brown in colour. Add the chopped tomato and lightly fry for about 10 minutes. Add salt and pepper (and a pinch of sugar if necessary). Cook over a low heat for a while and then puree in a blender.
Pan-fry the aubergines without any oil until lightly toasted.
Arrange a layer of aubergines on a tray, followed by a layer of tomato and then a layer of Parmesan cheese (or any other cheese that takes your fancy: burrata is to die for!) and repeat to use up the ingredients.
Finish with a layer of Parmesan cheese, sprinkle with oregano and bake at 180 °C for about 20 minutes.