1. At intervals, peel 3 lengthwise strips of skin from each eggplant, leaving it striped; cut each eggplant lengthwise into 6 slices. In a large bowl, dissolve ¼ cup coarse salt in 2 quarts water. Add the eggplant, push it down to submerge it, and soak for at least 30 minutes. Rinse and drain the eggplant and pat dry. With the point of a knife, make a series of small slits along the edges of half of the eggplant slices.
2. Meanwhile, put the lentils in a small conventional saucepan, add enough water to cover by at least 2 inches, and bring to a boil. Reduce the heat to medium and simmer until the lentils are about half cooked, 15 to 20 minutes. Drain the lentils and set aside.
3. In a mixing bowl, combine the grated tomatoes, onion, garlic, 2 tablespoons of the mint, the green chile, red pepper paste, tomato paste, Marash pepper, 1 tablespoon coarse sea salt, and black pepper.
4. Brush the cazuela with 1 tablespoon of the olive oil. Arrange the snipped eggplant slices over the bottom in a single layer. Top with half of the lentils and half of the tomato mixture; repeat with the remaining eggplant, lentils, and tomato. In a small bowl, whisk together the pomegranate molasses and remaining olive oil; drizzle over the top.
5. Cover and bring to a boil; remove the over and cook over low heat for 1 ½ hours. Remove from the heat and let cool for at least 2 and up to 6 hours. Serve at room temperature, with the remaining shredded mint scattered on top.
If using an electric or ceramic stovetop, be sure to use a heat diffuser with the clay pot.