1/4 cup extra virgin olive oil, plus more for serving
1/4 teaspoon salt
1/2 teaspoon sesame seeds (for garnish)
parsley (for garnish)
Heat a grill over medium heat. When hot, place eggplant directly on the grates and grill, turning every 10 minutes, for a total of 30-35 minutes. Eggplant should be creamy on the inside, while the outer skin will be thin and crispy. Remove and place on a large plate or baking sheet, cover with aluminum foil, then let sit for 20 minutes.
Carefully slice each eggplant in half and scoop the flesh into a large bowl. Discard any bits of skin that fall in with the flesh. Place eggplant in a strainer over a large bowl and let sit for 10 minutes to remove any excess liquid. Return eggplant to a clean bowl.
Add lemon juice and garlic and stir mixture quickly with a fork or whisk until smooth and creamy, about 2 minutes. While stirring, slowly add tahini and olive oil. Taste and add salt as needed.
To plate, transfer babaganoush to a serving bowl. Top with a drizzle of olive oil, some sesame seeds, and parsley for garnish. Serve warm or at room temperature with pita chips or crudité.