In soup pot or large saucepan, sauté onion in olive oil until translucent, about 8 minutes. Add ginger, cumin, cayenne, and salt; stir 1 minute. Add sweet potatoes and stir to coat. Stir in broth and coconut milk and bring to boil; reduce heat and simmer, covered, 15–20 minutes, or until sweet potatoes are tender.

Working in batches, purée soup in blender until smooth (an immersion blender will yield a more rustic purée). Return soup to pot, stir in lime juice, and season with additional salt, if desired. Serve, garnished with cilantro leaves.