According to an article in The Times, if you stick a spring onion with a root in a glass of water, you can cut bits off the top and it will carry on growing.
Not entirely sure of the logic of this, as there is no soil to draw nutrients from. Still, worth a try.
Next – potatoes in the bath.
After Work 
Similar, perhaps, to cress on blotting paper. Maybe there are enough minerals in the water ? The “control” would be to try the same experiment with distilled water ?
P.S. I believe the Antarctic Survey have had similar success with herbs on cotton wool soaked in melted snow.