Is it possible to record the video feed out of the Apple TV’s new capability of using iOS device camera to see the video feed on Apple Music?

(Longest question ever, I know)

So I’ve been playing around with the new feature on tvOS to use my iPhone camera to see oneself on the tv screen when singing along Apple Music tracks. But I can’t for the life of me figure out how to record what’s on the screen.

Is it even possible? If so, how?

Thanks.