I KNOW pat bing su didn't originate in Japan. Asian origins might be Malaysian, Korean or Filipino. If I had to guess Asian, I'd guess Filipino -- ice as an integral part of anything usually means Americans were there. But, as I say, NOT Japanese. If I had to bet though, I'd bet American sno-cones converted to Hawaiian "shave ice," and worked their way west to Asia. But they could have come to Hawaii from the Phillipines.
Just go ahead and use teh Google for "pat bing su," "patbingsu," and "pat bing soo," and you'll get all the variations. You can pick up an inexpensive ice shaver and all the good stuff at any decent Asian market. Green tea is one variation, and by no means a necessity. At this time of the year, as a chaser for Korean barbecue, I'd probably go melon or citrus.