Preheat oven to 200°C. Spray a large rectangle baking tray with olive oil and line a large baking tray with baking paper.
Place the eggplant in a single layer on the prepared tray. Spray with olive oil and season with cracked pepper. Bake for 10 minutes or until tender.
Spray a large non-stick frying pan with olive oil and set over medium-high heat. Add onion to the pan cook for 1-2 minutes, or until just softened. Add lamb mince, garlic and oregano, cook, stirring for 2-3 minutes, or until mince is browned. Add the zucchini, carrot, potato and chopped tomatoes, and bring to the boil. Reduce heat to low and simmer for 5-6 minutes or until sauce thickens.
While meat mixture is cooking, combine yoghurt and egg in a small bowl and set aside. Spread over half the meat mixture on the base of the prepared dish and top with half of the eggplant slices. Repeat by using the rest of the meat sauce and eggplant. Pour the yoghurt and egg mixture over the top of the moussaka to evenly coat.
Crumble over the feta and bake in the oven for 10-15 minutes or until golden.
While Moussaka is cooking, bring a small pan of water to the boil. Add the broccolini and simmer for 4 minutes until tender. Drain.
Serve Moussaka with steamed broccolini.