The first thing I did was to consult the ladies on the Sense and Sensibility Forum. They are always a treasure trove of historical costuming knowledge. Suzi Clarke, a reputable costumier from the UK, directed me to the Kannik's Korner pattern image, here. Look at View A, Round Eared Cap. That's the style I was going for. She also guided me as to how to cut the fabric to get the shape I wanted. You can see the layout above...
I decided early on that I wanted to hand sew the cap. Hand sewing is, after all, the method that would have been used during the Regency era. I started by sewing up the ties, and then turning them right side out, as seen in the above image. Then, I hemmed and gathered the front ruffle, and sandwiched it between the inner and outer layer of the brim. The brim is the only part of the cap that is essentially, "lined."
I also placed the ties inside of this "sandwich", and then did a sort of running, back-stitch to sew up the top edge and sides.
Once done, I turned the brim right side out, and folded in the seam allowance on the bottom edge. Here it is before the main portion of the cap was sewn on.