Grill the whole eggplants over the flame of a gas stove or on a rack set over an electric cooktop until the skin is charred all over, a couple minutes each side. Put the eggplants in a large bowl and cover tightly with plastic wrap to steam for 8 to 10 minutes. When cool enough to handle, remove the charred skin and discard, reserving any liquid in the bowl.
Roughly chop the eggplant flesh and put in the bowl along with any reserved eggplant liquid. Add the tahini, lemon juice, yogurt and garlic, then season with salt. Mash with a fork until thoroughly combined. The dip can be stored in an airtight container in the refrigerator up to 3 days.
Transfer the dip to a serving dish and top with pomegranate seeds, crushed walnuts, parsley leaves and a drizzle of olive oil. Serve with pita bread for dipping.