Preheat an oven to 400 degrees F. Lightly grease a baking sheet.
While the oven is preheating, slice eggplant in half lengthwise. Use a fork to poke a few dozen holes on the skin side of the eggplant. Sprinkle flesh with 1/2 teaspoon salt and let sweat 10 minutes. Rinse and pat dry. Place eggplant flesh side down on prepared baking sheet.
Cut the tip of the garlic off to expose cloves inside. Place garlic onto a square of aluminum foil. Drizzle a little of the olive oil over the exposed garlic cloves and wrap tightly with foil. Place garlic on the sheet pan with the eggplant. Drizzle remaining olive oil over eggplant.
Roast in the preheated oven for 30 to 40 minutes until eggplant is tender.
Use a large spoon to scoop the flesh from the eggplant and place in a food processor. Gently squeeze garlic cloves out of their peels and into the food processor.
Add in lemon juice, tahini paste, and remaining 1/2 teaspoon salt. Puree until smooth.
Transfer to a bowl and refrigerate 2 hours before serving.
Sprinkle with parsley to serve and drizzle on additional olive oil, if desired. Serve with pita chips or pita bread.