1. Pour oil into a 4- to 6-quart pan over medium-high heat. When hot, add onion, garlic, and ginger; stir often until onion is limp, about 5 minutes. Add curry powder, cumin, and cayenne; cook until fragrant, about 1 minute.
2. Add garbanzos, carrots, sweet potato, and broth; bring to a boil. Reduce heat to maintain a simmer, cover, and cook, stirring occasionally, until vegetables are tender when pierced, 30 minutes.
3. Whirl in batches in a blender or food processor until smooth. Return to pan and stir in lemon juice and salt and pepper to taste. Heat until steaming, then ladle into bowls.