Place the eggplant slices in a colander and sprinkle evenly with the salt.
Allow them to sit for 30 minutes to release excess moisture. Rinse the slices thoroughly under cool water, until no noticeable saltiness remains, and pat dry with a clean kitchen towel.
Heat the frying oil in a wide skillet over medium heat. After 90 seconds, when the oil is hot, add the eggplant slices in a single layer without crowding the pan. Fry over medium heat for 3 to 4 minutes per side, until golden and tender. Transfer the fried eggplant to a plate lined with a clean towel to absorb excess oil. Repeat with the remaining eggplant, adding more oil to the pan as needed and allowing it to reheat for 90 seconds before adding more slices. Set the fried eggplant aside.
To prepare the sauce, heat the olive oil in a saucepan over medium heat. After 90 seconds, when the oil is hot, add the garlic, cumin seeds, ground coriander, cardamom, turmeric, and Aleppo pepper flakes. Cook over medium heat for 1 minute, stirring constantly.
Add the diced tomatoes, tomato paste, brown sugar, and salt. Stir thoroughly to combine. Bring the sauce to a simmer over medium heat, then reduce the heat to low and cook uncovered for 8 minutes, stirring occasionally, until the sauce thickens.
For the herb yogurt, combine the plant-based yogurt, lemon zest, garlic, mint, parsley, and salt in a small bowl. Stir thoroughly until evenly mixed.
To assemble, spread a thin layer of the herb yogurt at the bottom of a serving dish. Layer spoonfuls of the tomato sauce and the fried eggplant slices over the yogurt. Spoon additional sauce and herb yogurt over the eggplant, ensuring all slices are well coated.
Serve the eggplant warm or at room temperature, garnished with parsley leaves, dried mint, and finely minced red onion.