So I had to try it. For this first attempt I dug around for some yarn I didn't care about, and found some really fat, scratchy green wool. Rug yarn maybe? I didn't follow one of her patterns, just did the amazing and original möbius cast-on. I knit a few (double) rounds, alternating 2 rows of knit and 2 rows of purl. Cat Bordhi recommends a 45" circular needle. I used the longest one in my stash (30") and it was awkward. Don't even think about using anything shorter.
It worked! What you want to notice in this picture is how the circular needle is coiled into two loops, rather than the regular circle. It's definitely one of those knitting projects in which you just have to have faith and follow directions, abandoning any need to make sense of what you're doing.
The basic deal is to use a very long circular needle, cast on stitches, knit once around, then knit around again picking up the other side of those same cast-on stitches. (You do a stranded cast-on, which just becomes another row of knitting.) That maneuver coils the cable of the needle into two loops. You place a marker to show the beginning of a round, but on each round you do two loops. You sort of say "Hi!" to your marker after the first loop, as it's at the bottom edge of your knitting. But then it shows up again on your needles after finishing the second loop (or one full round).
Confused? I did my best to explain that clearly, but it's a non-trivial problem, as we say in computer geek speak.
Your cast on becomes the "spine" of the piece, and on each full round you add a row on either side of that spine. That shows up well when you do a round in a contrasting color. You can see it in my cast-off. I used the suggested I-cord cast-off, in gray yarn.
Both sides of the cast-on will show, so the I-cord is a nice choice since it's the same back & front.
This looks like it might make a nice neck-wrap, but no one wants this scratchy stuff against their skin. I think I'll try one of the felted bowls. I'll pick up stitches from the I-cord (in green), going around only one loop. Then I'll cut across, picking up stitches through the green bit, then along the I-cord and back to my first picked up stitches. This will leave me with a twisted brim for my bowl. I'll knit round and round, decreasing to nothing at the bottom, and then felt it. Stay tuned!