Place potatoes and ginger in large saucepan. Pour in chicken stock and water, and bring to a boil over high heat. Reduce heat to medium low, cover, and simmer until the potatoes have softened, about 30 minutes.
Puree potatoes and lime juice in a food processor, or with a hand blender until smooth. Return soup to saucepan and stir in milk or cream as desired; heat until warmed through.
