The pattern for the 1-color brioche hat demonstrated in the video is below. Also at the bottom are additional helpful video links for this hat project. I used a small needle to get a tighter fitting, beanie-like hat. You can choose to vary the needle size and the yarn, but would suggest making a small flat swatch using the 1-color brioche pattern (slightly different than the "round" pattern; link to a video on this: https://youtu.be/4E0rLm3_jXU) and then checking the width of that swatch. You want the hat circumference to be about 20-21 inches for an adult size hat.
Abbreviations: BRK=brioche knit; BRP=brioche purl; DPN=double-pointed needles; K=knit; K2Tog=in this pattern knit the st and the brioche stitch next to it together; P=purl; Sl1=slip 1 stitch; Sl2=slip 2 stitches; SM=slip the st marker; st=stitch; YF=bring yarn to the front; YO=yarn over
Materials – Yarn: ImpeccableTM Loops & Threads brand 100% acrylic, one 4.5 oz skein (if doing a the one-color hat, but using 2 colors for stripes, then use 1 skein of each color); Needles: US size 3 (3-3.25 mm) circular needle and a set of 4 DPNs of the same size; 1 stitch marker; tapestry needle
Cast on 64 st using the US size 3 circular needle. Place a stitch marker after the last st cast on and join in the round when doing the set-up row.
Set-up row: yf, *Sl1, YO, P1. Repeat from * until you reach st marker. Then sm and start on Row 1.
Row 1: *BRK, YF, Sl1. Repeat from * until you reach st marker. Then sm and start on Row 2.
Row 2: YF, *Sl1, YO, BRP. Repeat from * until you reach st marker.
Then sm and repeat rows 1 and 2 until hat measures about 7 inches from the cast on edge (ie, the brim; it may be better to knit this part a little bit longer to avoid having a short hat, so can knit up to about 1-1.5 inches from the desired full hat length). Transfer stitches equally onto 3 DPNs and then follow the steps below for shaping the crown.
Shaping the crown
Row 1: *BRK, K2Tog, YF, Sl1. Repeat from * until you reach st marker.
Row 2: *YF, Sl2, YO, BRP. Repeat from * until you reach st marker.
Row 3: *K2Tog, YO, Sl1. Repeat from * until you reach st marker.
Row 4: YF, *Sl1, YO, BRP. Repeat from * until you reach st marker.
Repeat Rows 1-4 until you have 12 st (count a brioche stitch as 1 st). Then K2Tog to give you 6 st. Snip off a 6 inch tail and using the tapestry needle, pull the yarn through the remaining 6 st and pull. Re-insert yarn through center to bring it to the wrong side of the hat and weave the end. Optional step would be to add a pom-pom at the top.
(For the large stripped hat shown in the video, I alternated the light and darker green colors, each time switching after a Row 2 was done for the previous color)
Link to Long-tail cast on video: https://youtu.be/EiSK1gqqNz4
Link to Magic loop circular knitting video: https://youtu.be/08LH40HhHms
Link to Stitch transfer from circular needles to DPNs: https://youtu.be/rLG4r-Sw1qk
Link to Hat crown finishing: https://youtu.be/rLG4r-Sw1qk