Grill the eggplant till the outsides are really charred and the flesh inside has become soft. (I do it on the stove top but you can use an oven or a charcoal fire). Cover with a cloth and keep aside for 2 minutes.
Peel the skin off while still warm; cut and chop the flesh roughly.
Place in a mortar and pestle, food processor or grinder and add garlic, tahini, yoghurt and half of the lemon juice. Blend for a minute or two. Season with salt, taste and adjust the quantities of tahini, yoghurt and lemon juice.
Transfer to a large serving plate and drizzle the olive oil on top. If you prefer a creamier consistency, add the olive oil and blend again.