Char the eggplants over a gas flame or grill, turning often, until the skin is blackened and the flesh is very soft, about 10–15 minutes. Alternatively, roast them in the oven at 450°F (230°C) for 30-40 minutes, turning occasionally.
Once cool enough to handle, peel off the skin and discard it.
Finely chop the flesh using a knife until you reach your desired texture. Avoid using a blender.
Make the tahini mixture by stirring together the tahini, yogurt, lemon juice, pomegranate molasses, garlic and salt in a bowl. Mix until smooth. If the mixture is too thick, add a little ice-cold water to loosen it.
Combine the chopped eggplant with the tahini mixture and stir until well blended.
Serve on a plate or shallow bowl. Drizzle with olive oil and garnish with pomegranate seeds, sumac, and fresh herbs if desired. Serve with warm pita bread.