Preheat oven to broil or BBQ or grill to high and line baking sheet.
Prick eggplant all over with a fork to allow liquid and steam to escape. Place on foil lined baking sheet and broil for about 30 minutes, depending on size of eggplant. Eggplant should be tender and skin charred. You want to be able to pierce flesh easily with fork.
Once cooked, transfer eggplant into colander fit over bowl to drain and cool completely before removing skin. Larger eggplants will release more fluid and this liquid will make a very watery babaganoush.
Scrape all flesh from eggplant, discarding any liquid that has drained from eggplant. Transfer to food processor along with tahini, remaining ingredients. I do suggest starting with 1/2 clove of garlic and 3 Tbsp lemon juice and add more after tasting.
Blend or pulse to desired consistency; I like mine a little chunky.