This is still, without a doubt, some of the best bingsu I've ever had. I was lucky enough to eat this while filming a documentary called 'Taste of Korea' with National Geographic (Check out the video here : http://www.vingle.net/posts/438145)
Bingsu is traditionally made with shaved ice, pat (red bean) and occasionally ice cream and is served with Korean rice cakes. This fantastic variant was served with a tasty assortment of nuts on top and the ice flakes were made from frozen condensed milk which made the whole taste much richer.
I wish I could go back but I have no idea what the café was called ㅠㅠ I shall have to head back to Jeonju next time and try to find it!