Prepare a charcoal grill for direct heat.
Pierce some holes in the skin of the eggplants with a fork. (Skip this step and odds are good your eggplant will explode in a very messy way.)
Place eggplants directly on hot coals and turn with tongs every 1-2 minutes, until skin is charred and flesh is very soft, 8-10 minutes. Remove form the coals and carefully wrap each eggplant tightly in plastic wrap. Set aside to cool for 1 hour.
Without removing the plastic, cut the stem end off of the eggplants and squeeze the flesh out like toothpaste into a colander placed in your sink. Pick out any larger pieces of charred skin (smaller bits are ok), and drain for 30 minutes.
Transfer the flesh into a food processor along with the garlic, lemon juice, tahini, salt, and pepper, and process 10-15 seconds, scraping the sides of the bowl as needed. Add the parsley and pulse a few times to combine.
Serve room temp with pita chips or refrigerate up to 3 days.