Pierce each eggplant once or twice with a fork. Gas stove method: place whole eggplants directly on the burner grates over high flame. Turn with tongs every 3–4 minutes until skin is charred and collapsed on all sides — about 12–15 minutes. Broiler method: place on a baking sheet under a broiler at maximum heat for 25–30 minutes, turning once or twice, until skin is dark and wrinkled and eggplant collapses when pressed.
Transfer charred eggplants to a bowl and cover tightly with plastic wrap. Leave 15 minutes. Cut each in half and scoop out the flesh with a spoon, discarding the charred skin.
Place flesh in a fine mesh sieve or colander over a bowl. Leave 10 minutes to drain. Press gently to remove more liquid. Do not skip this — excess liquid makes the dip watery.
Transfer drained flesh to a large bowl. Mash with a fork to a rough, slightly chunky texture — not a smooth puree. Add tahini, lemon juice, grated garlic, olive oil, salt, cumin, and smoked paprika. Stir until fully combined. Taste and adjust — more lemon if flat, more smoked paprika if smoke is mild.
Cover and refrigerate for at least 30 minutes before serving. The flavor improves significantly with resting time — make it several hours ahead or the day before for best results.
Spread onto a wide plate. Drizzle generously with olive oil. Scatter fresh parsley, smoked paprika, and red pepper flakes on top. Serve with warm pita or flatbread.