Step 1 Spray a large saucepan with oil and cook onion and carrot over a medium heat, stirring occasionally, for 6-7 minutes until vegetables are soft. Add garlic and cook for 1 minute.
Step 2 Add mince and cook, breaking up with a wooden spoon, for 5 minutes. Drain any excess fat from pan. Add tomato paste, stirring, for 1 minute, then add tomatoes. Bring to the boil then reduce heat to low and simmer for 10 minutes or until thick. Season to taste and remove from heat.
Step 3 Meanwhile, spray a large chargrill pan or frying pan with oil and place over a high heat. Chargrill eggplants, in batches, for 2 minutes each side until lightly charred and tender.
Step 4 In a small bowl whisk yoghurt, egg and feta until well combined. Season to taste.
Step 5 Spoon one-third of the lamb mixture into the base of a 1.5-litre (6-cup)-capacity ovenproof dish. Top with one-third of the eggplant slices to evenly cover lamb. Repeat with another 2 layers of lamb and eggplant. Spread yoghurt topping over the top layer of eggplant and bake for 35-40 minutes until topping is golden brown. Serve with steamed vegetables.