Who is the musical group that performed at the end of an David Letterman show that I am describing (they performed probably in the 2000s)?

There was a musical act that closed a David Letterman episode quite a few years back. It might have been in around 2000s or even before in the 90s.

The act had a soulful brunette girl as the singer, and 3 or so guys playing instruments in her band. One was piano and one was a saxaphone I think.

I am trying to find the names of either song/artist/episode of it. It was on youtube at one point, and probably is still, but I can't find it.

I do remember at the end of her performance, David Letterman was very impressed and said something like "Do you want to grab a steak" to the singer.