A customer once asked me to construct a hat he had seen in a Kurosawa film. The result is this WWII aviator-style hat, with both a visor and an earflap that folds up without the assistance of snaps or ties.
The embroidered flame on the front is echoed on the back of the earflap. Shown here in recycled denim with a fur-lined earflap, it will work equally well in wool or other fabrics. I offer additional embroidery motifs as well.