Preheat your oven to 400°F (200°C).
Slice the eggplant into half-inch rounds and lightly brush with half of the olive oil.
Place eggplant on a parchment-lined baking sheet and roast for 15 minutes until tender and slightly browned.
While eggplant roasts, heat the remaining olive oil in a skillet over medium heat.
Sauté the diced yellow onion and minced garlic until translucent and fragrant.
Add the ground lamb to the skillet, breaking it up with a spoon, and cook until fully browned.
Stir in the cinnamon, oregano, sea salt, black pepper, and tomato puree; simmer on low for 5-7 minutes.
In a small bowl, whisk together the Greek yogurt, egg white, and ground nutmeg until the mixture is smooth and creamy.
In a small oven-safe baking dish, layer the roasted eggplant slices followed by the spiced lamb mixture.
Pour the yogurt béchamel over the lamb, spreading it evenly to the edges.
Lower oven temperature to 375°F (190°C) and bake the moussaka for 20 minutes until the topping is set and golden brown.