Heat the butter in a medium-size saucepan over medium heat. Add the sweet potatoes and green onions, cook, stirring, for two to three minutes. Add enough of the chicken stock just to cover the potatoes, and bring to a boil. Reduce the heat to medium-low, and simmer until the potatoes are tender, about 15 minutes.
Remove from the heat and pour the mixture into the bowl of a food processor. Puree the mixture, and then return it to the saucepan. Add the remaining chicken stock and simmer, stirring to blend. Season with salt, pepper, and Cajun seasoning. Cover and chill for about 3 hours.
To serve, add the crabmeat, heavy cream and garnish with the green onions.
Makes 6 to 8 servings