I first came across this when I discovered The Songwriters series on DVD. It's a short-lived TV series (on PBS, I believe), where composers performed their own songs and told the stories behind them. There are two shows to a DVD, and it's highly-worth checking out if you like this sort of thing. I haven't seen them all, so I can't attest to everything, but my favorites are Sheldon Harnick and Kander & Ebb. The one with Alan Jay Lerner is pretty good, as well. (The Netflix user ratings for the series is just mediocre, but don't be thrown off by that. I suspect it's related to the production values being limited, and the songwriters not being Professional Performers. But the best of them sing the bejeepers out of their songs.)
The one with Yip Harburg is a bit different. Unlike the others, he does almost no singing -- he knows his limitations -- but rather has a small combo of performers who do most of the honors. What he does provide are the entertaining stories about the songs. That makes it a touch less interesting than the other shows, though the songs themselves stand as pure gems.
One of the rare exceptions on the show is the opening number, which is...okay, you can probably guess. As is clear, he's no singer. As is equally clear, he knows "Over the Rainbow" inside and out, down to its depths, and understands every tiny nook of it. When he sings it, it's not the wistful longing of something he wishes could be, the lovely interpretation we're generally used to, but a heart-breaking plea for a better world he achingly wants to be, actually, real. He really wants to know, literally, if birds can fly why, oh, why can't he ? No, Yip Harburg can't sing. All he can do is make you feel like you're hearing one of the best-known and best-loved songs for the first time, and fall in love with it. And interestingly, by the end, he's allowed himself to get so carried away by the song, in a way that is so touching and impressive, considering that he wrote it about 35 years earlier and had probably heard several thousand times.
(Side note: His show is paired with Sheldon Harnick, which is appropriate because he was Harnick's hero and mentor. It was hearing Harburg and Burton Lane's Finian's Rainbow that got him interested in going to New York and becoming a lyricist.)
Happily, I was able to track down a video of just this one song from the show. The DVD is worth it (combined, as I noted, with Harnick's which is great), but for the time being this saves you the time of watching his whole episode just for these three, magical minutes.