Brimless, beret-style cap with a hatband.
This style, if it were white, would look like a floppy chef's hat. In color it makes a different statement and can be worn in many different ways. It can be worn like a snood, with all your hair tucked inside. It can be worn like a beret pulled down on side and pushed up on the other. You can pull it forward like a bill to shield your eyes from the sun. You can add a brooch and a feather to make it fancy. Best of all it can be folded up and stuffed in your pocket or pouch when you don't need a hat.