Wash the eggplants, peel them in alternating strips, and cut them into medium-sized cubes. Sprinkle with salt, rest for 20-30 minutes, and pat dry.
Preheat the oven to 400°F (200°C). Toss the eggplant with 2 tablespoons of oil and roast for 25-35 minutes until golden and tender.
Heat the remaining oil in a pot. Cook the chopped onion for 8-10 minutes until soft and golden.
Add turmeric, cinnamon, and black pepper. Stir briefly, then add the ground walnuts and cook for 2-3 minutes.
Stir in the tomato paste and sweet pomegranate molasses. Gradually add 1 1/2 cups of cold water.
Simmer the walnut sauce over low heat for 15-20 minutes, stirring occasionally. Add more water if needed.
Gently add the roasted eggplant. Cover partially and simmer for another 15-20 minutes until tender.
Taste and adjust the salt and pomegranate molasses. Rest for 5 minutes and serve warm with Persian rice.