In 4-quart Dutch oven or saucepan, heat oil over medium-high heat. Add carrots, sweet potato and onion; cook 6 to 8 minutes, stirring frequently, until onion is tender. Add curry paste, gingerroot and garlic; cook and stir 30 seconds. Stir in broth and coconut milk. Heat to boiling; reduce heat to medium-low. Simmer 10 to 15 minutes, stirring occasionally, until vegetables are tender.
Meanwhile, cook rice in water as directed on package. Add shrimp to vegetable mixture; cook 4 minutes longer or until shrimp are pink.
Serve shrimp mixture over rice in bowls. Sprinkle with basil.