Serve this Middle Eastern-inspired relish with toasted pita bread for a delicious snack or with a handful of other appetizers as a mezze course.
Heat broiler. Place eggplant on a baking sheet; pierce a few times with a fork. Cook, turning as skin blackens, until flesh is very soft, about 35 minutes. Remove from broiler; let stand until cool.
Scrape flesh into the bowl of a food processor, discarding skins. Add yogurt, pomegranate molasses, and lemon juice; season with salt and pepper. Pulse until mostly smooth, with just a few chunks.
Transfer to a serving bowl; stir in remaining ingredients. Cover with plastic wrap; chill until ready to serve.