Brioche looks far more complex than it is. It is basically slipped stitches and yarn overs.

This pattern is both written and charted (excluding the set up rounds and basic brioche rib). It is charted two different ways.

Yarn:
Single Color Hat
Three Fates Yarn chione dk 100% Merino; 250 yds/229 m per 115 g skein; Guinevere; 1 skein. (About 150 yards used)

Two Color Hat
Color A
Bumblebirch Quill 100% Merino; 231 yds/211 m per 100 g skein; Puddle; 1 skein. (About 90 yards used)
Color B
Bumblebirch Quill 100% Merino; 231 yds/211 m per 100 g skein; Fog; 1 skein. (About 90 yards used)

Dimensions:
18 (21)” / 46 (53) cm circumference (taken after blocking)
9” (12) / 23 (30.5) cm height (taken after blocking)
Gauge and needles:
17 sts / 24 rows = 4” / 10 cm in brioche rib on US 5 (3.75 mm) (see notes) 16” (40 cm) and preferred style for small-circumference circular knitting

Notions:
Stitch markers
Darning needle

Abbreviations:
sts - stitches
k - knit
p - purl
brk - brioche knit (knit the stitch with it corresponding yarn over)
brp - brioche purl (purl the stitch with it corresponding yarn over)
yf sl1yo - bring the working yarn to the right side, slip the next stitch, and yarn over the top of it. (The yarn over must sit on top of the slipped stitch which is why the yarn is brought forward before the slipped stitch.)
brkyobrk - brioche knit, yarn over, brioche knit into the same stitch (one stitch becomes three)
brk3tog - brioche knit three stitches together including corresponding yarn overs (three stitches become one)
brksssk - slip, slip, slip brioche knit including corresponding yarn overs (three stitches become one and slants the opposite way of brk3tog)
( ) - repeat

A cowl is forthcoming.