Preheat the grill. Prick the eggplant all over with a fork to prevent it bursting, place it on a tray and grill 10-15 minutes, turning regularly, until soft and charred.
When cool, slice the eggplant in half lengthwise and scoop out the insides. Mash the flesh in a bowl with a fork until smooth. Add 1 tablespoon olive oil, vinegar, garlic, salt and pepper and a little za'atar. Mix well.
Serve at room temperature with the other tablespoon of olive oil on top, and sprinkled with a little more za'atar.