In food processor, process carrots, onion, garlic and chile with 20 on/off pulses until chopped. In 4-quart saucepan or Dutch oven, heat oil over medium heat. Stir in chopped vegetables, curry powder, ginger, salt and bay leaves. Cook 10 minutes, stirring occasionally.
Meanwhile, in food processor, process thawed spinach with 10 on/off pulses until finely chopped. Add spinach to vegetable mixture. Stir in both cans of soup and the tomatoes until well combined. Cover; cook over medium heat 5 to 7 minutes, stirring frequently, until carrots are crisp-tender.
Meanwhile, in food processor, process cilantro with several on/off pulses just until finely chopped.
Remove saucepan from heat. Stir in cilantro and coconut milk. Remove bay leaves. Top individual servings with yogurt.