This is a pakul ( pakol, pakoul ) lambs wool hat. It is worn by the tribal men of Pakistan & Afghanistan. These quality wool "Freedom Fighter" caps are from the Chitral region of Pakistan. The cap part is fully lined with softer fabric that seems to be a cotton blend. The stitched flat top is slightly larger than the roll of the headband, causing folks to refer to these as "pie hats". Chitrali Pakul caps are worn as an alternative to the turban or skull cap.