Warm oil in a pot over medium heat. Add onion; sauté until softened, 6 to 8 minutes. Add ginger and garlic; sauté until fragrant, about 1 minute.
Raise heat to medium-high; stir in carrots. Pour broth into pot, cover and bring to a simmer. Remove cover, reduce heat to medium to maintain a simmer and cook until carrots are very tender, about 25 minutes. Remove soup from heat and let cool slightly.
Working in batches, purée soup in a blender until smooth. Transfer to a large bowl, cover and refrigerate until chilled, at least 2 hours.
Just before serving, stir in lime juice and yogurt. Season with salt and pepper. Serve chilled, garnished with lime wedges, if desired.