Preheat oven to 350 degrees F (175 degrees C). Line a baking sheet with aluminum foil.
Prick eggplants all over with a fork and place on the baking sheet.
Bake in the preheated oven, turning frequently, until soft, about 40 minutes.
Place eggplants on a cutting board and let stand until cool enough to handle, 8 to 10 minutes. Peel off skin and chop flesh.
Combine eggplant flesh, 2/3 cup Greek yogurt, garlic, 4 teaspoons chopped mint, lime juice, olive oil, salt, and pepper in a bowl; mix thoroughly. Spoon into a serving dish.
Dissolve saffron in a small bowl of hot water; drizzle over eggplant mixture. Garnish with mint leaves and 1 teaspoon Greek yogurt.
