That Annette Hanshaw recording was one of the first things I thought of when I saw the title of this thread. But there’s another one I don’t think has been mentioned...
The 1933 tune “My Bluebird’s Singing the Blues,” which was featured prominently in the film “International House.” Baby Rose Marie sings it in the movie, but the melody plays off and on throughout the film. But in terms of recordings of it, my preference is for the version done by the hot British band, Madame Tussaud’s Dance Orchestra, on the rare Edison Bell Winner 78rpm label, and with a female vocal. An obscure but fine band that apparently recorded only in that single year of 1933, and did some rather nice versions of some Duke Ellington tunes.