Rolf wanted a plain, neutral colored beanie. Looking through my stash, I identified the grey alpaca as a potential candidate, only that it is way too thin. However, I’ve nearly 3 full skeins and therefore tried holding it triple. With a needle size 4mm this results in a nice squishy, yet light fabric.

Here is how I made this
Casted on 12 stitches ( distributed on 3 DPNs), closed into the round, knit one round (R1).
R2: k1, yo
R3: knit all, the yo tbl - 24 stitches.
R4 to 7: 2 full brioche rounds. (R4: s1 p-wise with yo, k1)
Put claw markers on the 2nd, 6th, and 10th right stitch column.
R8: Brioche-increase 2 stitches (k, yo, k in the same stitch) in every 2nd knit stitch column, beginning with the first one.
R9: work each of the increase columns as: sl p-wise with yo, p, sl p-wise with yo.
R10 - R15: work three full brioche rounds.
R16: increase as above in the knit columns before and after the markers. Repeat R9 - R16 three more times - 84 stitches.
Continue brioche pattern without increases to the desired length, ending with a p1, sl1 with yo round

Brim fold
R1: p1, k1
R2-3: p
R4: k
R5: p
R6: p1, k1 with picking up the corresponding purl bump of the same column of stitches from R1 for each purl stitch (I.e. every second stitch). Do this by first slipping the stitch to the right needle, picking up the bump from R1 with the right needle, slipping both back to the left needle and purl both together.
Continue in brioche to the desired brim length.

Finishing
R1: p1, k1
Now 2 preparation rounds for tubular cast-off:
R2: sl1wyif, k1
R3: p1, sl1wyib
Finish with a sewn Italian bind-off.
Use the end from your cast on to stitch it through eve4y 2nd stitch of the cast on edge, pull tight, sew in all remaining ends.

Result
I think I made what he wanted - good!
Somehow, the brioche pattern created a bias, i.e. slanting to one side, even after blocking, not sure why that is, it annoys me a little.