In a food processor, combine cilantro, ginger, garlic, scallions, and process until finely chopped. Add sugar, oil and lime juice and mix well. Toss shrimp in mixture until coated. Cover bowl and chill 1 hour.
Spoon the shrimp out of marinade and saute lightly until cooked. Arrange on serving plate and chill.
Add reserved marinade to the liquid from the cooked shrimp stirring, until the liquid evaporates, leaving a thick green puree. Add cream and boil again, stirring constantly until thick. Do not reduce too much as this sauce thickens as it cools.
Pour sauce into a serving bowl and refrigerate with the shrimp until both are chilled and ready to serve.