Set eggplants on grill rack. Grill until skins darken and wrinkle on all sides, about 25 minutes for large globe eggplants, 20 for Italian, and 15 for Japanese, turning every 5 minutes. Cool 5 minutes.

Set small colander over bowl or in sink. Trim top and bottom off each eggplant. Slit lengthwise and scoop hot pulp into colander; let drain 3 minutes.

Transfer pulp to food processor. Add lemon juice, oil, garlic, tahini, salt, and pepper; process until coarse, about eight 1-second pulses. Adjust seasoning, cover, refrigerate 45 to 60 minutes. To serve, drizzle with olive oil, sprinkle with parsley.