Called garðaafelling (garter bind off) in Icelandic, this bind off has been known in Iceland at least since the middle of the 19th century. It was popularised among modern Icelandic knitters by Sígriður Halldórsdóttir who describes it in her book Þríihyrnur og langsjöl (Triangular and long shawls), a book on traditional Icelandic shawls, translated in English, first published in 1988. Sígriður notably taught it at the Handprjónasamband Íslands (Icelandic Handknitting Association) where it has been used ever since to bind off lopi sweaters collars.
I´ve been teaching this BO in my knitting tours since 2010 and through the years, it has spread worldwide under the name Icelandic BO. At the time, it seemed little known outside Iceland and the participants in my trips will have made it popular under this name and little by little it became known and taught under the name Icelandic BO in the knitting community worldwide.
This BO does not add an extra row and allows the sts to be BO in an elastic way, but only with the right tensioning! The longer the BO loop, the more elastic it is.
It goes like this: knit 1 st, *BO (pass the st over the next st), k the next st from the inside of the BO loop, then drop the 2 sts off the needle.* Rep between *-* until all sts are BO, drag yarn through the last loop.
Here is a little video: