The song Gilbran has mentioned seems very remniscient of this story (purportedly German in origin) titled "Elise's Vanity" about a miller's daughter who wishes to be beautiful and is told if she never looks at her face again then she will be beautiful. She does as told for several years, until one night she decides to look and dies in fright of being ugly again: https://newspapers.library.in.gov/?a=d&d=THDG18710311.1.3&e=-------en-20--1--txt-txIN-------

Here is a song-version of "The Broken Ring" to which Ged Fox referred: link

It does seem to have a similar pattern of song as this song (link) The miller's daughter = die Müllerstochter / text by Alfred Tennyson; music by Henry Bickford Pasmore.

None of those (except the short story) have the phrases Gibran is looking for, though.