Preheat your oven to 400°F. Slice the eggplant into 1/2-inch thick rounds and lightly brush both sides with olive oil.
Place eggplant rounds on a parchment-lined baking sheet and roast for 15-20 minutes until tender and lightly browned.
While the eggplant roasts, place a skillet over medium heat and brown the ground lamb with finely diced onion and minced garlic until the meat is no longer pink.
Stir in the tomato puree, cinnamon, oregano, sea salt, and black pepper. Reduce heat and simmer for 10 minutes until the sauce has thickened.
In a small mixing bowl, whisk together the Greek yogurt, egg, and parmesan cheese until the mixture is smooth and well combined.
In a small oven-safe baking dish, layer half of the roasted eggplant slices, followed by the lamb mixture, and then the remaining eggplant slices.
Pour the yogurt and egg mixture over the top, spreading it evenly to the edges.
Lower the oven temperature to 375°F and bake the moussaka for 20-25 minutes until the custard topping is set and develops a golden-brown color.