Preheat an outdoor grill for medium-high heat and lightly oil the grate. Using a fork, poke holes in the eggplant so steam will be able to release during cooking.

Place eggplant on the preheated grill. Grill until skins are charred, about 30 minutes, turning occasionally. Transfer to a baking pan, cover, and let steam for 10 minutes.

Using your hands, carefully remove the stem and the skin; the skin should be split open and peel off easily. Discard the skin and place flesh in a colander; let drain for 20 minutes. Press out any remaining moisture with paper towels.

Place eggplant in a food processor. Add tahini, lemon juice, za'atar, crushed red pepper, salt, paprika, and garlic. Pulse until smooth. Add olive oil and parsley; pulse until oil is incorporated. Garnish with additional crushed red pepper flakes and parsley if desired.