Prick the eggplants a few times with a fork. Char them directly over a gas flame or under a broiler, turning every few minutes, until the skin is blackened and the eggplants have collapsed, 20–30 minutes. Alternatively, roast halved eggplants cut side down at 450°F (230°C) for 35–40 minutes.
Transfer to a bowl, cover and let steam for 10 minutes.
Split the eggplants and scoop out the flesh, leaving the skin behind. Place the flesh in a sieve for 5 minutes to drain the bitter liquid.
Chop the flesh finely, or mash with a fork for a chunky dip; use a food processor for a smoother one.
Stir in the tahini, lemon juice, garlic, salt and cumin. Add the olive oil and mix well.
Taste and adjust the lemon and salt. Spread in a shallow bowl, drizzle with olive oil and sprinkle with parsley and paprika or sumac.