Roast the eggplant on open gas flame - range top or barbecue. If your stove is electric, split the eggplant lengthwise, place face down on cookie sheet and bake in hot oven on top rack 30-45 minutes. For open flame roasting, use a fork to turn often. Skin will wrinkle and char, and flesh will shrivel and become soft. When eggplant is completely soft all over, remove to a bowl, slash once or twice to drain out bitter juice, and let rest until cool enough to handle. Some authors suggest cooling the eggplant inside a brown paper bag.
Cut off stem and peel away skin. Scrape flesh into bowl of food processor or blender. Add garlic, tahini, lemon juice and process. Amounts depend upon size of eggplant and your taste - please sample frequently. Salt to taste.
If you don't have a food processor or blender, the eggplant is quite easy to mash by hand. Mash the garlic with the flat of a broad knife, then mince it fine. Some cooks prefer mashing by hand to mechanical means as the blades of food processors can break the seeds which releases undesirable bitter flavours. If you have a mortar and pestle, mash the garlic with salt into a paste. A large mortar and pestle can be used to mash all ingredients.
Serve at room temperature, drizzled with olive oil, garnished with a black or green Mediterranean olive, or sprigs of cilantro or parsley.