Charred Eggplant Soup with Cumin and Greek Yogurt

INGREDIENTS

• 1 Tbs. extra-virgin olive oil, plus more for grilling and brushing
• 2 large eggplants, about 2 1/2 lb. total, peeled and cut crosswise into slices 1 inch thick
• 3 ripe tomatoes, about 1 1/4 lb. total, cored, halved and seeded
• 3 carrots, peeled and finely diced
• 5 shallots, finely chopped
• 3 garlic cloves, minced
• 3/4 tsp. minced fresh thyme
• 1/4 tsp. ground cumin
• 1 cup fruity white wine
• 5 cups low-sodium chicken or vegetable broth
• 1 1/2 tsp. kosher salt, plus more, to taste
• Freshly ground pepper, to taste
• 1/2 cup plain Greek-style yogurt