Preheat grill to medium-high heat. Place eggplants and green onions onto the grate. Grill onions for approximately 3 minutes or until lightly charred and just tender. Turn occasionally. Remove from grill and cut into chunks.
Grill the eggplants over direct heat for 10-15 minutes or until skin is well charred, turn occasionally. After 10-15 minutes, move them to the indirect heat, the cool side of grill. Cover the grill and cook for another 20 minutes or until soft and tender. Cool 10 minutes or until they can be handled.
Remove the eggplant skin and scoop out the flesh. Remove the seeds if desired (I did this). Place the eggplant flesh, grilled green onions, garlic, tahini, lemon juice, cumin, smoked paprika, salt and pepper into the bowl of a food processor. Process until smooth scraping down the sides of the bowl as needed.
With the food processor on drizzle in the olive oil and purée until combined. Taste for seasoning then serve topped with a drizzle of olive oil, za'atar seasoning, smoked paprika and chopped parsley. Best served with grilled or warm pita bread or vegetable of choice.