This technique is often used to start the knitting of a shawl. It is a way of casting on the stitches around a small tab of garter stitch to avoid the formation of a "hollow" at the base of the shawl, in order to produce a nice uniform border.
This technique is referred as "Garter tab cast-on". That said, you will find my own version of this technique in the following video since I introduced the use of a NEKO cable needle and I use my left needle to pick-up the stitches on the left side of the garter tab. As a picture is worth a thousand words, discover all the details in this video: