This is Jessie Mueller showing up for Seth Rudetsky's videocast. I’m not fan of his at all, but she just blows you away here -- and even stuns him at the end.
The point of this episode is her uncommon talent of being able to sing in different styles and voices, shown off last year when she got a Tony nomination as Best Featured Actress in On a Clear Day You Can See Forever, when she performed as a jazz singer, and currently in her Broadway show, Beautiful, where she sings in a style that suggests Carole King. But as is explained in the video, she has this versatility to do so much more.
What so impressive here, though, is that as a rule, singers like to prepare and warm up and not just get thrown into singing -- but here this appears almost like she just popped in and is game for what he throws at it, and that's what makes the performance she gives all the more impressive. Now, in fairness, she likely got some forewarning and perhaps did a bit of warm-ups, but still, this isn't much more than a "pop-in" (as you can see below) and hardly a major performance, and ultimately this is just total seat-of-the-pants impressive work, because she has no idea what he's going to throw and her and is clearly game for it.
And as I said, even Rudetsky is blown away by what she does at the end...