Tightly wrap each eggplant in foil and place directly into the coals of a hot, dying fire. Roast for 40-50 minutes, rotating occasionally for even cooking. The outside of the eggplants should be charred and wrinkly.
Unwrap the eggplants from the foil and use a sharp knife to cut through the center of each eggplant. Use a spoon to scrape out as many fully formed seeds as you can.
Use the spoon to remove the eggplant flesh from the skin, placing it into a bowl. Discard the charred skins. Let cool.
Heat a small pan over medium heat. Add the sesame seeds and toast until they've darkened in color. Place the toasted seeds into a blender or food processor along with the olive oil. Blend until a smooth tahini sauce forms.
Stir garlic, cumin, lemon juice, salt, pepper, and fresh parsley into the eggplants, then transfer to a food processor. Pour in the tahini sauce and blend until smooth.
Let the baba ghanoush set until it reaches room temperature. Make a divot in the center, then pour in extra olive oil and sprinkle on green onion, parsley, and red pepper flakes, as desired. Serve alongside warmed pita bread and dippable vegetables. Enjoy!