Preheat your oven to 400°F and line a baking sheet with parchment paper.
Slice the eggplant into 1/2-inch thick rounds and lightly brush both sides with half of the olive oil.
Arrange eggplant on the sheet and roast for 15-20 minutes until softened and slightly browned.
While eggplant roasts, heat the remaining olive oil in a skillet over medium heat and sauté the diced onion and minced garlic until translucent.
Add the ground lamb to the skillet, breaking it up with a spoon, and season with cinnamon, oregano, sea salt, and black pepper.
Once the lamb is browned, stir in the tomato puree and simmer on low for 5-7 minutes until the sauce has thickened.
In a small mixing bowl, whisk together the Greek yogurt, egg white, and ground nutmeg until smooth.
In a small oven-safe baking dish, layer half of the roasted eggplant slices, followed by the lamb mixture, and then the remaining eggplant.
Pour the yogurt mixture over the top, spreading it evenly to the edges, and sprinkle with the parmesan cheese.
Lower the oven temperature to 375°F and bake the moussaka for 20-25 minutes until the topping is set and lightly golden.