Place the lamb mince, finely chopped onion, crushed garlic, dried oregano, dried mint, bay leaf, and cinnamon stick in a large heavy-based frying pan. Set over a medium heat and cook for 10 minutes, stirring frequently with a wooden spoon to break up any lumps. The meat should be fully browned and beginning to smell warmly aromatic from the spices. — Resist the urge to rush this stage — allowing the mince to properly brown rather than steam gives the sauce a deeper, richer flavour foundation.

Stir in the tablespoon of plain flour and season generously with salt and pepper. Pour in the red wine, canned chopped tomatoes, and tomato purée, stirring to combine. Bring everything up to a gentle simmer, then cook uncovered for 30 minutes, stirring occasionally, until the sauce has thickened considerably and the lamb is tender. The sauce should coat the back of a spoon and smell deeply savoury and spiced. Taste and adjust seasoning, then remove from the heat and set aside. — If the sauce reduces too quickly, add a small splash of water to prevent catching on the bottom of the pan.

While the meat sauce cooks, slice the aubergines into 5mm rounds and layer them in a colander. Sprinkle over the tablespoon of fine sea salt and leave to draw out moisture for 10 minutes. Rinse thoroughly under cold running water to remove the salt, then pat completely dry with a clean tea towel — this step prevents the aubergine from becoming soggy when fried. — Salting aubergine not only draws out bitterness but also firms the flesh, so it absorbs less oil during frying.

Heat 3 tablespoons of olive oil in a large heavy-based frying pan over a medium-high heat. Fry the aubergine slices in batches for 2–3 minutes on each side until deep golden and tender, adding more oil between batches as needed. The slices should be soft through the centre and richly caramelised on the surface. Transfer to a plate lined with kitchen paper to drain off excess oil. — Work in a single layer and avoid crowding the pan — overcrowding causes the aubergine to steam rather than fry, leaving it pale and oily.

Peel the potatoes and slice them thinly — around 3mm thick. Cook in a large pan of boiling salted water for 5 minutes until just beginning to soften but still holding their shape. Drain carefully into a colander and run cold water over them immediately to stop the cooking. The slices should be pliable but not falling apart. — Parboiling ensures the potatoes cook through fully in the oven without remaining raw or watery.

Preheat the oven to 200°C / 180°C Fan / Gas 6. To make the béchamel, melt the butter in a large saucepan over a medium heat. Stir in the plain flour and cook, stirring constantly, for about 30 seconds to form a smooth paste. Gradually whisk in the milk, a little at a time, ensuring each addition is fully incorporated before adding the next to avoid lumps. Stir in half the Parmesan and the grated nutmeg, then simmer gently for 4–5 minutes, stirring regularly, until the sauce is smooth, glossy, and thick enough to coat a spoon. Season with salt and pepper. — Warming the milk slightly before adding it to the roux makes the sauce come together more smoothly and quickly.

Remove the béchamel from the heat and allow it to cool for a few minutes. Once it is no longer piping hot, stir in the beaten egg thoroughly. This enriches the sauce and helps it set to a creamy, sliceable layer during baking. — Let the sauce cool sufficiently before adding the egg — if it is too hot, the egg will scramble rather than blend smoothly into the sauce.

Spoon one-third of the lamb sauce into the base of a large shallow ovenproof dish (approximately 2.5 litres capacity). Arrange roughly one-third of the potato slices over the top, followed by one-third of the fried aubergine slices. Repeat these three layers twice more, finishing with a final layer of aubergine on top. — The layers do not need to be perfectly neat — a relaxed, rustic arrangement is fine and means the moussaka holds together better when spooned out.

Pour the béchamel sauce evenly over the top of the assembled layers, using a spatula to spread it into a thick, uniform blanket covering the entire surface. Scatter over the remaining Parmesan. Transfer to the preheated oven and bake for 35–45 minutes until the top is deep golden-brown and the edges are visibly bubbling. The surface should be richly coloured and the cheese slightly caramelised. Remove from the oven and allow to rest for 10 minutes before serving. — Resting the moussaka before cutting allows the layers to settle and makes it far easier to serve in neat portions.