co 4 sts on dpns
join around, kfb into each of the 4 co sts
-easiest way for me to do this:
..co 2 sts on each of 2 needles
..kfb into first st with 1 needle, kfb into 2nd st with 2nd needle
..kfb into first st on 2nd needle with 3rd needle, kfb into last st with 4th needle
there should now be 2 sts on each of 4 needles
kfb first st of each needle as you knit around, until you have 15 sts on each (so 60 sts total)
knit around about 9 rows, or about 2 1/2 inches, or until flattened hat measures about 6 inches from top
kfb first st of each needle, one round
knit 2 rounds with no increases
repeat those 3 rows 2 more times
knit one more increase round which should give you 19 sts per needle
bind off, crochet a trim to prevent curling (in the example i single crocheted around twice, into the back loops only)
block as needed

if you don’t want a crochet edge, you could probably knit the last 4 or 5 rows in seed stitch instead.

depending on your yarn, you may want to use make 1 increases instead of kfb for the bottom section to prevent unwanted bumps.