Preheat the oven to 375°F.
Sprinkle the eggplant slices with salt and let them sit for about 30 minutes to draw out moisture. Rinse and pat dry.
In a large skillet, heat olive oil over medium heat. Add the chopped onion and garlic, sautéing until the onion is translucent.
Add the ground beef or lamb, cooking until browned.
Stir in the diced tomatoes, tomato paste, oregano, cinnamon, black pepper, and cayenne (if using). Simmer for about 10 minutes, then remove from heat.
In a mixing bowl, whisk together the Greek yogurt, eggs, and half of the Parmesan cheese until smooth.
In a greased 9x13-inch baking dish, layer half of the eggplant slices on the bottom.
Spread the meat mixture evenly over the eggplant, then layer the remaining eggplant on top.
Pour the yogurt mixture over the final layer of eggplant.
Sprinkle the breadcrumbs and remaining Parmesan cheese on top.
Bake for 45-50 minutes, or until the top is golden brown and bubbly.
Allow to cool for 10 minutes before serving.