This hat is sometimes called a Muffin hat or cap, its of the same family as a modern chef hats, a popular lower class Renaissance period hat (15th to 17th Century Europe)
Made from basic usually lightweight fabric with no natural stiffness, with a access fabric sewn to 20 to 50cm wide headband that fits tightly around the head.
A very simple and easy to produce hat, the headband can sometimes be decorated.
This hat has no stiffened brim unlike renaissance flat caps or cow pat hats
I grabbed this off my friend Dave just as he was about to trade it, the hat did not make it to the bring and buy.