Heat oil in a large skillet over high heat. Fry the eggplant slices in batches until golden brown on both sides, this would take about 5-7 minutes. Do not crowd the pan. There is no need for the eggplants to cook completely at this stage. Transfer to a cooling rack placed on a baking sheet and set aside.
Heat 2 tablespoons oil in a large skillet over medium heat. Add the diced tomatoes and cook for 4 to 5 minutes until they begin to break down. Add the minced garlic and cook 1 to 2 minutes more until fragrant.
Stir in the tomato paste, salt, black pepper, turmeric, and water. Cover and cook for about 15 minutes, mashing the tomatoes with the back of a spoon as they soften, until you have a thick rustic sauce.
Arrange the fried eggplant in the sauce and top with the sliced tomatoes. Spoon some sauce over the top, cover, and cook another 10 to 15 minutes until the eggplant is very tender and the tomato slices have softened.
In a bowl, stir together the yogurt, grated garlic, salt, and dried mint until smooth.
Spread the yogurt across a serving platter. Spoon the warm eggplant and tomato sauce over the yogurt and serve immediately with warm bread.