Preheat your oven to 400°F and line a baking sheet with parchment paper.
Slice the eggplant into 1/2-inch thick rounds, brush both sides with olive oil, and roast for 15-20 minutes until tender.
While eggplant roasts, sauté the diced onion and minced garlic in a non-stick skillet over medium heat until translucent.
Add the ground beef to the skillet, breaking it up with a spatula, and cook until browned.
Stir in the tomato puree, oregano, cinnamon, sea salt, and black pepper, then simmer on low for 10 minutes to thicken the sauce.
In a small bowl, whisk together the Greek yogurt, egg, and parmesan cheese until smooth to create the custard topping.
In a small oven-safe baking dish, layer half of the roasted eggplant rounds, followed by the beef sauce, and then the remaining eggplant.
Spread the yogurt custard evenly over the top layer of eggplant.
Bake for 20-25 minutes until the custard is set and the top is beautifully golden brown.
Let the moussaka rest for 5-10 minutes before serving to allow the layers to firm up.