Preheat your Air Fryer to 400 degrees Fahrenheit for five minutes. Cut the top off of the head of garlic and place it at the center of a square of aluminum foil. Brush a teaspoon of olive oil on top of the exposed cloves, then wrap the whole bulb in the foil and set aside.
Poke the eggplants a few times with a fork. Place them into the basket of the preheated Air Fryer along with the prepared head of garlic and cook for 25-30 minutes at 400 degrees, turning once halfway through cooking. The eggplant is done when it is charred on the outside and creamy on the inside. The garlic should be soft and release easily from the papery peels.
Once the eggplants are cool enough to touch, slice them in half and use a spoon to scoop the flesh away from the skins. Discard skins, reserving a few small pieces to add to the baba ganoush, if desired.
Place the eggplant flesh (and skin, if using) into the bowl of a food processor or blender. Add the tahini, lemon juice, yogurt, salt, and two tablespoons of olive oil. Add half of the garlic cloves to the bowl (reserve the rest for another use). Process the eggplant mixture until pureed and smooth. Taste and add more salt or lemon juice to suit your taste.
Transfer to a serving bowl and top with additional olive oil, sumac, toasted pine nuts, and fresh herbs if desired.