Heat a little olive oil in a saucepan, add mince and onion and cook and stir until browned. Season with salt and cayenne pepper. Stir in the tomato purée and the water. Cover and simmer for 30 minutes.
Preheat oven to 190 C / Gas 5. Grease an ovenproof casserole dish.
Lightly fry the aubergine in a light drizzle of oil. Transfer to kitchen paper and blot away any excess oil.
Put a layer of aubergines in the base of the prepared casserole dish, sprinkle with 200g grated cheese and cover with a further layer of aubergines and then the mince mixture.
Pour the béchamel sauce over and sprinkle with the remaining cheese.
Bake in the oven for 20 to 30 minutes, until bubbling and the cheese is golden brown.