Preheat a grill to medium. Prick the eggplant all over with a fork. Grill, turning frequently, until the skin is charred all over, 10 to 15 minutes. Transfer to a cooler part of the grill and continue cooking until the eggplant is very soft, 5 to 10 minutes. Transfer to a bowl and let cool slightly.
Peel the eggplant and discard the skin and any juices. Mash the eggplant with a fork, then beat in the yogurt, tahini, lemon juice, garlic and cayenne; season with salt. Top with the parsley and drizzle with EVOO.
Grill the pitas until warm; cut or tear into eighths. Serve with the baba ghanoush and olives.