Heat oil in large skillet over medium heat. Add onions and ginger and cook until onions are softened, about four minutes. Add coconut milk and chicken broth and bring to a simmer; cook uncovered until slightly thickened, about four minutes. Whisk in curry paste. Add prawns and fish sauce and cook just until prawns are opaque in center, about three minutes. Transfer to serving dish; stir in grapes, lime juice and basil.
Serve with cooked rice.
*Available at Asian markets and in the Asian food section of some supermarkets.