In a large saucepan simmer the carrots, leeks and potatoes in the broth with the ginger, cinnamon, allspice, salt and pepper to taste, covered, for 30 minutes, or until the vegetables are very tender. In a blender or food processor puree the soup in small batches, transferring it to a large bowl, stir in the cream, and chill for at least 4 hours up to overnight. Season with salt and pepper and serve cold.