Can you help me find this singer using very little information?

A few years ago I saw a man singing on TV. I always want to look up names like “Jason Mraz” or “James Blunt” when I try to find him, so I think his name may start with a J… or he may have a similar sounding music style.
I am fairly sure it was Letterman’s show, but not positive. He played the piano, not a guitar, and was wearing a hat like this. The song that he sang was a cover, but I did not know the song… only that I liked his interpretation.

I know the odds of anyone knowing what I’m talking about are very slim, but, I’ve seen stranger things happen here. Any ideas?