Preheat the oven to 450°F (230°C).

Prepare the eggplant: Wash and dry the eggplants, then cut them into 1½-inch cubes. If the skin is tender, leave it on. Alternatively, peel off a few strips for a zebra-pattern effect.

Roast the eggplant: In a large bowl, toss the eggplant with 2 tablespoons olive oil and ¼ teaspoon salt until evenly coated. Spread on a parchment-lined baking sheet and roast for 30–35 minutes, or until fork-tender. Check after 20 minutes and adjust the cooking time as needed. Set aside to cool slightly.

Sauté the onions: Heat the remaining olive oil in a large cast-iron casserole dish or Dutch oven over medium heat. Add the onions and cook until soft and lightly golden, about 10–15 minutes.

Add the spices: Stir in the turmeric, black pepper, dried mint, advieh (or cinnamon), and remaining salt. Cook for 1–2 minutes, stirring constantly, until fragrant.

Add the walnuts: Stir in the ground walnuts and cook for 1–2 minutes. Add the pomegranate paste, tomato paste, and lemon juice. Cook for another 2–3 minutes, stirring frequently.

Simmer the stew: Pour in 3–4 cups ice-cold water. For a richer stew, add a few ice cubes, which may help encourage the walnuts to release more oil. Bring to a gentle boil, then reduce the heat to low. Cover and simmer for about 20 minutes, until the sauce thickens and a light layer of oil begins to appear on the surface.

Finish the stew: Gently fold in the roasted eggplant. Simmer uncovered for 10–15 minutes, until the eggplant is fully heated through and the stew reaches a thick, rich consistency.

Serve warm with Persian saffron rice, steamed basmati rice, or flatbread.