This stitch is different from regular brioche! The original image was so inaccurate, I had to knit it to see it for myself. It’s from 1870 Mrs. Beeton’s Guide to Embroidery, Crochet and Knitting, p.148. The pattern has only 1 row with a multiple of 3 stitches +1 extra stitch. I added 2 selvage stitches that you can omit, if preferred. With 1 row, this pattern is truly reversible.
Blocked aggressively in #10 crochet cotton, German Brioche makes a net-like fabric. Blocked gently in worsted weight yarn, the fabric is thick and cushy.

Skills needed: cast on, slip, knit, k2tog, YO and bind off in knit stitch.

Gauge is not important in this pattern. Any block-able yarn/thread will work. Make a swatch to check gauge and appearance.

50 yards of Lion Brand 24/7 yarn will make 10 inches of a 33-stitch-wide strip at gauge.