Pierce eggplants in several places with a fork and grill on a rack set 5 to 6 inches over glowing coals, turning them occasionally, until very soft, 30 to 40 minutes. (Alternatively, broil eggplants under a preheated broiler about 6 inches from heat 30 to 40 minutes. Broiled eggplant will not have a smoky flavor.)
Transfer eggplants to a colander and when cool enough to handle, quarter lengthwise. With a small knife remove and discard as many seeds as possible. Scrape flesh into a large sieve set over a bowl, discarding skin. Drain eggplant, covered and chilled, 1 day. Discard any juices from eggplant.
Mince onion and garlic and finely chop parsley. In a food processor pulse eggplant with onion, garlic, parsley, and remaining ingredients until coarsely pureed. Transfer spread to a bowl and season with salt and pepper. Chill spread, covered, at least 3 hours and up to 3 days.