Cut eggplants in half lengthwise. Place on a jelly-roll pan, cut sides up; brush cut sides with 1 tablespoon oil. Broil 15 minutes or until tender and browned. Remove from oven; cool on pan 10 minutes. Peel eggplants; chop pulp. Place pulp in a bowl.
Finely chop 1 cup parsley; set aside. Combine remaining parsley, 2 tablespoons oil, onions, vinegar, garlic, and pepperoncini pepper in a food processor. Process until smooth, scraping sides of bowl occasionally; add to eggplant. Stir in reserved chopped parsley, capers, salt, and black pepper. Cover and chill 2 hours.
Spoon yogurt onto several layers of heavy-duty paper towels; spread to 1/2-inch thickness. Cover with additional paper towels; let stand for 5 minutes. Scrape yogurt from paper towel into eggplant mixture; stir gently.