After a little poking around this morning, I found this gem. Yes, it is really John Barrowman singing The Doctor And I, a parody of "The Wizard And I" from Wicked. Jack Harkness is a great character. According to a comment, Barrowman knew the composer of the original song and got permission to change the lyrics. I wish I could get it on iTunes, but from what I understand it was a special release on iTunes UK a year or so ago. I don't know if it's still available.
And now I'm wishing again that the new Torchwood episodes weren't on STARS. Sigh.