I suppose I should refine this into a how-to. Everything here is hand sewn so no expensive/dangerous machinery is required. For this project you will need a tailors tape (floppy ruler tape) and a non-stretch fabric like muslin or a 100%cotton bedsheet/pillowcase. A pen or pencil, needle and thread, whatever your final fabric is, and a pinch hubris.
Using the tailors tape, measure the circumferance of your head, divide that number by 6, and add one inch to this number for seam allowances. This will be the base/bottom of your triangular pattern panel. Now measure over your head from your forehead to the back of the head where you want your cap to sit. Check this against your above ear measurement, ear to ear. Pick the smaller measurement, divide by 2, and add 0.5 inch for seam allowance. Trust me, you can add more fabric later. Now take these measurements and make a flat bottom triangle, then fatten the diagonal edges like so
I've found that the fat edges help it conform to the shape of the head.
Use a ruler to measure 1 inch across at the top and make a dot in the middle.
This is your sew-to dot. Now duplicate this 5 more times. I would suggest making an accordion fold to get 5 layers of fabric, lay this pattern on top, and cut the other 5 layers out all-at-once. Sew them all together, along a the 0.5 inch seam allowance we added, using a basting stitch, from the base to the sew-to-dot, and try it on to see how it fits. (Fit simulated with the help of my apprentice, because I already ripped a panel back out.)
Adjust as needed to get something that conforms to the head without making a point. You want that nice fitted look. Guestimate however much length you think you need at the bottom to make it sit at the ears, add an inch to that, and that will be the additional ease you add to the bottom of the pattern when cutting your final material. The ease allows you to hem or roll as you please, and should be cut vertical with no taper, angle, or curve. Take the new piece you've cut, and cut 5 more pieces just like it! Sew them together (I prefer a back stitch for durability and stretch). Reenforce the point with stitches that go ACROSS the point, from one side of the head to another, and trim the additional seam allowance from the point to keep it from bulging. Finish the seams flat using your method of preference and try it on.
Trim/roll the hem for fit and flip it right side out! Done!
You can do this with only four panels as well. A hat is a hat. Add trim, fur, fingerloop braids, embroidery, a lining, an additional layer of insulation, whatever you like. The original burial find had wirework of gold!
Both of these examples have a felt inner layer for insulation and structure. The left is wool with wool felt and silk thread. The right is cotton with random felt moving blanket I saved from the work dumpster and poly fur. I believe it was cotton felt but I could be wrong.
Both have a linen lining using the same pattern as the outer. It makes it super easy to dry them after hand washing because they hang like this. Point a fan at your hat and leave it overnight.
You can also change the shape of the triangle to make different hat shapes. This one has more straight/vertical length on the sides of the panel coming up from the base, then tapering to a point, making almost a flat top with points at the corners. Now go make yourself a custom fitted hat for all the swag of a medieval noble!
What was that? An eldritch vision, rats in the walls, or the ghost of the brother you murdered!?
You too can creep through your manor at 3am with a candle, a robe, and a look of madness.
Do try not to fall from any windows. Do not pick a ground floor window if you do. Panache is important.
