Preheat your oven to 400°F and slice the eggplant into 1/2-inch thick rounds.
Arrange eggplant slices on a parchment-lined baking sheet, brush lightly with olive oil, and roast for 15 minutes until softened.
While the eggplant roasts, finely dice the onion and mince the garlic.
In a non-stick skillet over medium heat, brown the ground beef with the onion and garlic until the meat is cooked through.
Drain any excess liquid from the skillet, then stir in the tomato puree, oregano, cinnamon, salt, and pepper.
Reduce heat and let the beef mixture simmer for 5 minutes to allow the flavors to meld.
In a small mixing bowl, whisk together the Greek yogurt and the egg until the mixture is completely smooth.
In a small oven-safe baking dish, layer half of the roasted eggplant, followed by the beef mixture, and then the remaining eggplant.
Spread the yogurt and egg mixture evenly over the top layer of eggplant.
Lower the oven temperature to 375°F and bake the moussaka for 20 minutes until the topping is set and lightly browned.