1. Start a charcoal or wood fire, or preheat a gas grill (or the broiler); the rack should be no more than 4 inches from the heat source. Cut the eggplants in half lengthwise up to the stem, but do not cut through, so the eggplants open like a book. Spread about 2/3 of the onion and garlic between the eggplant halves, and press the two sides back together.
2. Grill the eggplants, turning once or twice, until they are blackened and collapsed, 10-15 minutes. Don't worry if the skins burn a bit.
3. Meanwhile, mix the remaining onion and garlic with the yogurt; then season with salt, black pepper, and cayenne.
4. When cooked, let the eggplants cool a bit, then peel off the skins and let cool further. Roughly chop the eggplants, reserving any juices, then mix with the yogurt dressing. Chill if time allows, or just serve at room temperature; garnish with mint or parsley.