Cook the rice in a saucepan of lightly salted boiling water for 20 minutes until tender.
Meanwhile, heat the oil in a large frying pan, add the courgettes and aubergine and cook over a high heat for 5 minutes, then add the lamb and cook for a further 10 minutes until the meat is browned.
Add the fresh tomatoes and cook, stirring, for 2 minutes, then add the canned tomatoes and bring to the boil. Reduce the heat, cover and simmer for 5 minutes.
Drain the rice and place in a bowl, then mix in the egg and two-thirds of the cheese. Season well.
Spoon the lamb and vegetables into a shallow gratin dish, then spoon the rice mixture over the top. Scatter with the remaining cheese. Cook under a preheated hot grill for 2–3 minutes until golden. Serve hot with a rocket salad, if liked.