1. Heat sesame oil in a Dutch oven over medium heat. Add ginger; sauté 30 seconds. Add curry paste; sauté 30 seconds. Add 1 cup broth, whisking until curry paste dissolves; add remaining broth and water. Bring broth mixture to a boil; cover, reduce heat, and simmer 10 minutes.
2. Add coconut milk and next 5 ingredients. Bring to a boil; reduce heat, and simmer, uncovered, 3 minutes or until chicken is done. Stir in cilantro. Ladle soup into individual bowls. Serve with lime wedges.