Sprinkle cut sides of eggplant with salt. Let stand for 20 to 30 minutes. Blot dry with paper towels.

Preheat an air fryer to 400 degrees F (200 degrees C).

Brush cut sides of eggplant with 1 tablespoon olive oil. Cut off the top 1/4 inch from the garlic bulb, exposing the cloves. Brush cloves with 1/2 tablespoon olive oil and wrap bulb in aluminum foil. Place eggplant and garlic in the air fryer basket.

Cook in the preheated air fryer until eggplant and garlic are tender and eggplant is deep golden brown, 15 to 20 minutes. Remove and allow to cool, about 10 minutes.

Scoop flesh from eggplant and place into the bowl of a food processor. Add tahini, lemon juice, 4 cloves of roasted garlic (reserve remaining roasted garlic for another use), remaining 4 tablespoons olive oil, cumin, and paprika; pulse to a moderately smooth consistency. Top with feta cheese, parsley, and lemon zest.