I wouldn't fancy having to notate her version. First of all is the lack of strict time. It can be done but I find it brain numbing. Then she isn't singing the tune. She is improvising melodically on the tune of EM's original. Every phrase is embellished and every repeat of a melodic line will be different. It wouldn't just be a matter of notating one verse and using repeats. You'd have to notate the whole thing. Not for me.

Don't get me wrong, I'm not criticising her performance. It's gorgeous. Notating it would be a nightmare.

Learning it by ear would be a good exercise but I guess the request for notation means that ear work is not an option. What she does here, both with voice and with her piano work, shows mastery of musical understanding, not only in a technical sense but also emotionally too. Aim high. Good luck.