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Heat the grill to high. Brown the beef in a deep ovenproof frying pan over a high heat for 5 mins. Meanwhile, prick the aubergine with a fork, then microwave on High for 3-5 mins until soft. Mix the yogurt, egg and parmesan together, then add a little seasoning.
Stir the tomatoes, purée and potatoes in with the beef with some seasoning and heat through. Smooth the surface of the beef mixture with the back of a spoon, then slice the cooked aubergine and arrange on top. Pour the yogurt mixture over the aubergines, smooth out evenly, then grill until the topping has set and turned golden.