Heat olive oil in a skillet over high heat. Add the eggplant strips and fry until softened and golden brown on both sides. You may need to do this in batches of 3-4 strips at a time.
In a fresh pan or skillet, heat olive oil over medium heat. Add the ground lamb and onion, and sautée until brown. 5-10 minutes.
Add the minced garlic, tomatoes, salt, black pepper, cilantro, oregano, cinnamon, and cumin. Stir in well and allow to simmer, stirring occasionally until the sauce has thickened. 15-20 minutes.
Preheat oven to 375°F (190°C)
Apply cooking spray to baking dish. Line the base of the dish with one layer of eggplant strips. Gently pour cooked lamb over eggplant, compressing and leveling with a spoon or spatula. Add another layer of eggplant strips over the meat.
In a separate bowl, add eggs, Greek yogurt, kosher salt, and black pepper. Whisk until creamy. Pour over eggplant and sprinkle grated parmesan on top. Bake for 40 minutes.
Remove from oven and allow to cool for 5 minutes before serving