Once was one of these movies. Particularly the music!!! It's all about the music.
The musician/actors pictured, Marketa Irglova and Glen Hansard wrote and sang all the songs in the movie which went on to win an Oscar in 2007 for Best Original Song. It is a bit quirky, understated and I loved it even more for the unknown actors, un-polished, low budget feel. Put it on your must watch list if you haven't already seen it!!