I found this image on Pinterest. Unfortunately, I couldn't trace the source of the image. The hat is blue with white beads.
These images are from an unreferenced Italian painting (pages 110-11 in 'What Life Was Like At The Rebirth of Genius", Time Life Books. ISBN: 0-7835-5461-3.) A similar style of padded roll can be seen in some Spanish paintings at around 1500 C.E.
I trimmed it to a rectangle in a size to fit my head, and sewed it into a tube. I then turned the fabric right side out and stuffed it with polyfill. In period, stufffing options would probably have included down, bombast, sawdust, wool or rags/fabric offcuts. I like the polyfill because it is light, cheap and easy to obtain.
I joined the ends of the tube together, adjusting the polyfill inside as I went, and adding a little more near the end. (A big knitting needle is a great tool for this step.)
When the roll was sewn up, it needed to be rolled around and adjusted to improve the shape.
I found that I hadn't made it quite big enough for my head, so I stretched it for a few days on a bucket.
I roughly measured and chalked where I wanted the lines of beads to go, and then started stringing. I used 4mm glass seed beads in white on a double strand of strong thread. I anchored one end of the thread, put all the beads on my string, and then sewed the other end into place. Then I came back through the centres of the beads with my thread again, anchoring it down with a stitch where I started. Then I went through and secured the main thread down between all the beads with a small stitch. I didn't extend the lines of beads all the way around because I find that my hair tends to catch and pull on beads.
The next step was to add the beads in the centre of the lines. I decided on three lots in each space, and three beads in each motif. I sewed each bead into place individually.
Checking the hat against the inspiration!
The finished product!
And views of the inside of the roll.
It is a very comfortable hat!