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 season with a pinch of salt and pepper.
Roast the eggplant for 15-20 minutes until tender and slightly browned, then remove from the oven and lower the temperature to 375°F.
While eggplant roasts, heat a non-stick skillet over medium heat. Add the ground lamb and diced onion, cooking until the lamb is browned and onions are translucent.
Stir in the minced garlic, dried oregano, and cinnamon, cooking for 1 minute until fragrant.
Add the crushed tomatoes and simmer the mixture for 8-10 minutes until the sauce has thickened; season with the remaining salt and pepper.
In a small bowl, whisk together the Greek yogurt, egg, and ground nutmeg until the mixture is smooth and well combined.
In a small oven-safe baking dish, layer half of the roasted eggplant, followed by the lamb mixture, and the remaining eggplant slices.
Pour the yogurt and egg mixture over the top, spreading it evenly to the edges.
Bake for 20-25 minutes until the custard topping is set and turns a beautiful golden brown.