Preheat your oven to 400°F and line a baking sheet with parchment paper.
Slice the eggplant into 1/2-inch thick rounds, lightly brush with olive oil, and roast for 15 minutes until tender and slightly browned.
While eggplant roasts, heat a skillet over medium heat and sauté the diced onion and minced garlic until translucent.
Add the ground lamb to the skillet, breaking it apart with a spoon, and cook until browned through.
Stir in the tomato puree, cinnamon, oregano, sea salt, and black pepper, then simmer for 10 minutes until the sauce has thickened.
In a small bowl, whisk together the Greek yogurt, egg, grated parmesan, and nutmeg until the mixture is smooth and velvety.
Reduce oven heat to 375°F and grease a small oven-safe baking dish.
Layer half of the roasted eggplant in the bottom of the dish, followed by the lamb sauce, and then the remaining eggplant.
Pour the yogurt béchamel over the top layer of eggplant, spreading it evenly to the edges.
Bake for 20 to 25 minutes until the topping is set and develops a beautiful golden-brown color.
Let the moussaka rest for 10 minutes before slicing to allow the layers to set perfectly.