This morning these were in the stores again. In Chinese they are called 雪莲果 (xuě lián guǒ), which literally translates as 'snow lotus fruit'. They are Smallanthus sonchifolius or Peruvian ground apples. In Spanish, yacón. The reason they look like root vegetables is because that is what they are! They are just a sweet variety and are eaten like a fruit, despite being the roots of a daisy-like plant. They are OK, but I wouldn't miss them if they never showed up again.
The larger one in the centre was around 11 inches in length.