A good part of its magic came from the music that Ben Stiller included. I started to look into the soundtrack and found the name José González.
José González is a singer-songwriter from Sweden. Besides his solo career he was part of some bands and projects, in particular Junip and Zero 7.
2007 In Our Nature
2007 Zero 7 - The Garden
2010 Junip - Fields
2013 Junip - Junip
2013 The Secret Life of Walter Mitty OST
2015 Vestiges & Claws
2019 José González & The String Theory - Live in Europe
If you want to listen to him, I'd recommend to start with "Vestiges & Claws" (2015) or "Live in Europe" (2019).