Preheat the oven to 425°F (220°C) or heat a grill to medium-high. Pierce the eggplants a few times with a fork.
Roast or grill the eggplants for 35-40 minutes, turning occasionally, until the skin is charred and blistered and the flesh is very soft.
Let the eggplants cool slightly, then slice in half and scoop the flesh into a colander. Let drain for 10 minutes to remove excess liquid.
Transfer the drained eggplant flesh to a bowl or food processor. Add the tahini, lemon juice, garlic, olive oil, and cumin. Mash or pulse until mostly smooth but still slightly textured.
Season with salt to taste. Transfer to a serving bowl, drizzle with olive oil, and garnish with fresh parsley and pomegranate seeds if using.
Serve with warm pita bread and olives on the side.