Make the meat sauce. Place the aubergines, onions, garlic, stock and wine in a large nonstick saucepan. Cover and simmer briskly for 5 minutes.
Uncover and cook for about 5 minutes until the aubergine is tender and the liquid is absorbed, adding a little more stock if necessary. Remove from the heat, allow to cool slightly, then purée in a food processor or blender.
Meanwhile, brown the mince in a nonstick frying pan. Skim off any fat. Add the aubergine mixture, tomatoes and pepper to taste. Simmer briskly, uncovered, for about 10 minutes until thickened.
Make the cheese sauce. Beat the egg whites with the ricotta, then beat in the milk and 4 tablespoons of Parmesan. Season to taste with pepper.
Alternate layers of meat sauce, lasagne and cheese sauce in an ovenproof dish. Start with meat sauce and finish with cheese sauce. Sprinkle the top layer of cheese sauce with the remaining Parmesan. Bake in a preheated oven, 180°C (350°F), Gas Mark 4, for 30–40 minutes until browned.