With the rack in the middle position, preheat the oven to 375°F (190°C). Line a baking sheet with parchment paper.
On a work surface, cut the eggplants in half lengthwise. With a small knife, score the flesh of the eggplant in a crisscross pattern, without piercing the skin. Season with salt and pepper.
In a large non-stick skillet over medium-high heat, brown the eggplant in the oil, cut side down. Transfer the eggplant to the baking sheet, cut side up. Bake for 45 minutes or until the eggplant is very soft. Set aside.
Meanwhile, in a skillet over high heat, brown the meat, onion and garlic in the oil, crumbling the meat until cooked through. Add the tomato and spices. Season with salt and pepper. Cook for 2 minutes, stirring constantly. Deglaze the skillet with the vinegar. Adjust the seasoning and set aside, keeping the meat warm.
In another non-stick skillet over medium heat, brown the bread crumbs in the butter. Remove from the heat and add the Parmesan. Combine thoroughly and let cool.
In a bowl, combine the yogurt and lemon juice. Season with salt and pepper.
On each plate, place an eggplant half. Top with the meat mixture. Garnish with the yogurt, bread crumbs and mint.