Preheat oven to 400°F and line a baking sheet with parchment paper.
Slice the eggplant into 1/2-inch thick rounds, brush with olive oil, and roast for 20 minutes until tender.
While eggplant roasts, sauté the diced onion and minced garlic in a skillet until translucent.
Add the ground lamb to the skillet, breaking it up with a spoon until fully browned.
Stir in the tomato puree, sea salt, black pepper, and ground cinnamon; simmer for 10 minutes.
In a small bowl, whisk together the Greek yogurt, egg, and parmesan cheese until smooth.
In a small baking dish, layer half the eggplant, then the lamb mixture, then the remaining eggplant.
Pour the yogurt custard over the top and bake for 20-25 minutes until the top is golden and set.