It's the song tarigwa argues is a ballad non-classic in the comments below and which I linked there because she performs it with the host, a singer/songwriter/++ who started out in the early 90s, and that fit with our talk of IU aligning herself with a certain crowd of artists.

I'll embed it here


(one of the Korean-language commenters on youtube is saying that she's too young to know 'old love', the title of the song)