1. Heat grill to high (450° to 550°) with an area left clear or turned off for indirect heat. Pierce eggplant in several places with a knife. Grill eggplant over indirect heat, covered, until very tender, 20 to 30 minutes. Let stand until cool enough to touch; meanwhile, continue with recipe.
2. Toast about 1/2 tsp. cumin in a small, dry frying pan over medium heat until fragrant and beginning to darken, 2 to 3 minutes. Pound fine with a mortar and pestle.
3. Warm oil in pan over medium heat. Sauté onion 3 minutes. Add garlic, then sauté until both are softened, about 2 minutes more. Let cool slightly.
4. Slit eggplant lengthwise and scrape flesh from skin. Chop flesh coarsely and set aside.
5. Combine yogurt, onion mixture, cilantro, and sugar in a bowl. Add eggplant and stir gently. Season to taste with salt, cumin, and cayenne. Garnish with a little more cilantro.
Make ahead: Through step 4 up to 1 hour; hold at room temperature.
Note: Nutritional analysis is per 1/2-cup serving.