He had me at the reveal as well. It took some moments of reflection to realize he didn't cut all the way through the carrot on all those initial slices. When he then peels off the ply, he gets a sheet with the requisite slits.
One of the subtle bits that's easy to overlook is that there's a wooden skewer through it to act as a knife stop. In case you want to do this yourself.
Also I'm guessing that the carrot was parboiled to make it softer.