Step 1

Season eggplant slices evenly with 1 tablespoon salt, and let stand, allowing excess water to drain, at least 30 minutes or up to 1 hour. Pat slices dry with paper towels. Heat 1/2 cup vegetable oil in a large skillet over medium. Working in batches if necessary, add eggplant slices to skillet, and cook until golden brown on both sides and very soft, about 10 minutes per side. Remove eggplant slices from skillet, and transfer to a plate lined with a single layer of paper towels to absorb excess oil. Transfer cooked eggplant slices to a bowl; mash with a fork until mostly smooth.

Step 2

Heat remaining 1 tablespoon vegetable oil in a smaller skillet over medium. Add onion, and cook, stirring occasionally, until lightly browned (do not caramelize), 8 to 10 minutes. Add garlic, and cook, stirring often, until garlic is fragrant, about 2 minutes. Add turmeric, and reduce heat to low; cook, stirring constantly, until onion mixture is coated with turmeric, about 30 seconds. Add mashed eggplant to onion mixture, and stir to mix thoroughly. Add 2 cups kashk to eggplant mixture, and stir until well combined. Add remaining 1/2 teaspoon salt. Cook eggplant mixture over low, stirring often, until mixture just begins to simmer, about 5 minutes. Remove from heat, and transfer mixture to a serving dish.

Step 3

Combine 1 teaspoon hot water and remaining 2 tablespoons kashk in a small bowl, stirring well to dilute slightly; set aside. Stir together saffron and remaining 1 teaspoon hot water in a separate bowl until well combined; set aside.

Step 4

Heat olive oil in a small skillet over high. Add dried mint to hot oil, and cook, stirring constantly, until fragrant, about 45 seconds, being careful not to burn mint. Pour hot mint mixture over prepared kashke bademjan. Add diluted kashk around mint mixture, and drizzle saffron drops on diluted kashk. Serve with toasted barbari or lavash.