Seed stitch on bias, but in two unique yarns!
The reddish yarn is linen, which has a dry and crisp appearance. Linen would usually be a bad choice for a headband because it stitches out as it is worn, but in this case, you can simply tie it a bit tighter as it stretches.
The second yarn (grey) is a wool crepe yarn. It has overtwist, which means is tends to want to twist itself up as you use it, and once you get it wet, the fabric transforms and twists around and it no longer looks like seed stitch!

While the techniques used are easy (knit, purl, make one, k2tog/ssk), the yarns are both tricky. It will take a couple rows for your fingers to adapt, but the end result is worth it!