Chef John's Baba Ghanoush

Preheat an outdoor grill for medium-high heat and lightly oil the grate. Prick the surface of the skin of eggplants several times with the tip of a knife. Place eggplants directly on grill. Turn frequently with tongs while skin chars. Cook until eggplants have collapsed and are very soft, 25 to 30 minutes. Transfer to a bowl and cover tightly with aluminum foil and allow to cool, about 15 minutes. When eggplants are cool enough to handle, split them in half and scrape flesh into a colander placed over a bowl. Drain 5 or 10 minutes. Transfer eggplant to mixing bowl. Add crushed garlic and salt; mash until creamy but with a little texture, about 5 minutes. Whisk in lemon juice, tahini, olive oil, and cayenne pepper. Stir in yogurt. Cover bowl with plastic wrap and refrigerate until completely chilled, 3 or 4 hours. Taste to adjust seasonings. Stir in mint and parsley.