Pre-heat the oven to 175° C. Slice one aubergine lengthwise thinly. Place the slices in a colander, sprinkle with a little salt and set aside for half an hour. Rinse with plenty of cold running water and firmly squeeze a few pieces at a time to draw out most of the moisture. Pat dry with a paper towel. Slice the other aubergine in half lengthwise and place the halves on a non-stick baking sheet, cut side down. Bake until soft (about 20 minutes).
Pat the salted aubergine slices dry and grill in a lightly greased pan (use a minimum of oil) until they are golden brown and crispy. Transfer to a plate and sprinkle with a little pepper. Scoop the baked aubergine flesh from the skin and transfer to a bowl.
Fry the prawns on high heat with the chopped basil, red onion, garlic and a little salt and pepper. Lower the heat and stir in the baked aubergine and a dash of white wine. Simmer for five minutes.
Transfer the prawn mixture to a bowl and combine with the seasoned breadcrumbs and most of the Parmesan cheese into a thick, evenly mixed filling.
Top the aubergine slices with a spoonful of filling and roll up the slices. Place the roll-ups in a baking dish, sprinkle lightly with the rest of the Parmesan cheese shavings and bake for a few minutes until the cheese melts.