Just listened to Hugh Lauries version of this for his upcoming album and it reminded my of how wonderful this song is. It would be great to see a comprehensive lesson for this and I think it would also provide a good platform for improvisation teaching/learning/practicing.
There's a great version of this by Dr John as well called "St Touro Infirmary". Its on the album "Dr John plays Mac Rebennack Vol.2" if anyones interested in having a listen.