Set up a medium fire in the barbecue grill.
Place the eggplants and the sliced onions on the grill. Grill the eggplants, turning occasionally, until the skins are blistered and the pulp begins to soften -- about 12-15 minutes. Grill the onion slices until light brown -- about 5 minutes per side. As each is done, remove from the grill and place on a plate.
Brush the pita rounds with olive oil, sprinkle with cumin and grill over the fire until lightly browned (about 1 minute per side). Remove from the grill and cut into quarters.
Split the grilled eggplants in half and scrape out the pulp into a blender or food processor, trying to avoid the charred skin. Add the grilled onion slices and process until the mixture is smooth.
Add the yogurt, garlic, lemon juice and tahini and puree the mixture well. Season with salt and pepper.
Transfer the eggplant/yogurt mixture to a serving bowl, sprinkle with parsley and tomatoes, and pour the olive oil over the top.
Serve the dip with the grilled pita. Leftover dip can be covered and refrigerated for about 3 days.