Preheat oven to 400°F and slice the eggplant into 1/2-inch thick rounds, arranging them on a parchment-lined baking sheet.
Lightly brush the eggplant slices with olive oil and sprinkle with a pinch of salt, then roast for 15-20 minutes until tender and slightly browned.
In a skillet over medium heat, brown the ground lamb with the diced yellow onion and minced garlic until the meat is cooked through.
Stir in the tomato puree, cinnamon, oregano, salt, and pepper, then simmer for 10 minutes to allow the flavors to meld and the sauce to thicken.
In a small bowl, whisk together the Greek yogurt and egg until completely smooth to create the protein-rich béchamel sauce.
In a small baking dish, layer half of the roasted eggplant slices, followed by the lamb mixture, and then the remaining eggplant.
Pour the yogurt béchamel over the top, spreading it evenly to the edges, and sprinkle with the parmesan cheese.
Bake at 375°F for 20-25 minutes until the topping is set and beautifully golden before serving.