The Snap-T (its original name) goes by a few different names and has a few different variations--the Pulley Cast, The Windcutter Cast, the Snap-C, the Circle Cast are four that you'll often hear. This past summer when I met with Dec Hogan to test his new line of rods he told me the story of its development:
The original cast was developed back in the late 80s by Washington State steelie guides John Farrar and Dec Hogan. Both saw a casting demo by Tom White at a trade fair. During the demo White would use the "snap" motion to draw his line back towards him so that he could catch it to change flies, fix wind knots, or simply make an impression on the audience. Farrar and Hogan thought they might by able to do something with this move and a Spey rod. Farrar messed about with the basics, combining the "snap" with a single Spey, and showed it to Hogan. Hogan worked on refining it, and the two soon after showed it to Sage Rep George Cook, who named it the Snap-T. At the time the guys were using shooting heads with their Spey rods (the original custom made versions of what was to become the RIO Windcutter) and when Vincent came out with the WC the line and method were brought together as a potent casting tool on the Winter steelhead rivers. Later guide Scott O'Donnell modified the cast into the Snap-C or Circle Cast, and Ed Ward has come up with a variation that I believe is known as the Periwinkle. I should note that although the cast is seen most often used with WC lines, it also works quite well with long-bellied Spey lines although you need to adjust your set-up and timing.
In the "casting videos" section of my web site there is some footage of Dec Hogan making a reverse Snap-T for those that are interested.