Didn't know it was a song. I heard the story with a Russian provenance. Only it was nail soup. Beggar claims to be onetime cook to the Tsar, fallen on hard times. Begs a little water and use of the fire, offering to teach lady how to make soup from a nail. He has the nail, but it's better if you put a bit of cabbage in. The Tsar particularly liked it that way. Then the Tsarina liked it with a bit of onion and potato. And, the Tsarevich liked a little meat in it...

I take it, this is the same story.