Chop the potatoes into 2 cm cubes (no need to peel). Put in a pan and cover with boiling water. Pop on a lid and bring to the boil. Simmer for 5-7 mins till the potatoes are just soft when pierced with a knife. Drain and set aside to dry.
While the potatoes cook, chop the aubergine into 2 cm cubes. Peel and finely chop the onion. Peel and grate or crush the garlic.
Heat a frying pan for 1 min. Add 2 tbsp oil and the aubergine. Stir and cook for 4-5 mins till golden on most sides. Tip into a bowl.
Keep the pan on the heat and add the beef mince. Cook for 3-4 mins, stirring with a wooden spoon to break up any lumps. Add in the onion and garlic. Season with salt and pepper. Cook and stir for 3 mins till the onion is just glossy.
Add the aubergine back to the pan with the cooked potatoes. Sprinkle in ½ tsp dried oregano. Stir. Pour in the chopped tomatoes. Half fill the can with warm water and add that too. Season and stir. Cover and simmer for 10 mins till thickened slightly.
While the mince is cooking, make your topping. Beat 1 egg in a bowl. Tip in the yogurt. Crumble in half the pack of feta. Add ½ tsp dried oregano and season with plenty of black pepper. Mix together. Heat your grill to its highest setting.
Taste the mince and adjust the seasoning. If your pan isn’t ovenproof, pour the mince mixture into an ovenproof dish. Spoon over the feta and yogurt topping, spreading it to the edges. Pop under the grill for 10 mins till browned and set. Serve on warm plates with a handful of salad leaves.