If possible, cook the eggplant on a grill/barbecue, turning now and then until it has blackened on all sides and is tender inside - time will depend on your grill but around 10-15min. If you can't grill it, you can do the same by placing it on a skewer and cooking over a gas flame on the stove or put it in an oven dish and bake around 15min at 450F/230C. In all cases, lightly brush it with olive oil before cooking.
Allow the cooked eggplant to cool enough to handle then peel off and discard the skin.
Place the eggplant flesh in a food processor/blender and add the rest of the ingredients (garlic - chop a bit first to save getting lumps, lemon juice, olive oil, tahini and salt and pepper). Pulse a few times until fairly smooth but still with a bit of texture. Try it and adjust seasoning to taste.