Pre-heat oven to 450.
Wrap garlic loosely in foil.
Put garlic cloves and eggplant on baking sheet with a rim.
Roast until eggplant and garlic are soft and eggplant skins begin to blister and blacken, about 45 minutes.
Remove garlic from oven; set aside.
Raise oven temperature and broil eggplant until skins are charred, about 3 minutes).
Transfer to wire racks; cool completely.
Heat oil in a small non- stick skillet over medium-low heat until hot, but not smoking.
Add sliced onion. Cook, stirring occasionally, until soft and golden ( about 8 minutes).
In a large bowl, whisk together chopped onion, yogurt and lemon juice.
Squeeze roasted garlic pulp into your yogurt mix; stir well.
Cut eggplant in half lengthwise.
Scrape flesh into a large, fine sieve placed over a large bowl; drain 15 minutes. Discard liquid.
Stir eggplant and salt into yogurt mixture;
Top with reserved cooked onion.