Fez

The Traveling Merchant is the only source, and his stock rotates, so getting one comes down to catching him on a day he happens to be carrying it. There is no way to save up for a specific hat. Check what he has every morning he turns up and buy it the moment you see it.

It reads as the last piece of a Doctor Who costume. The Eleventh Doctor spent a lot of screen time insisting that fezzes were cool, and most people buying this are assembling that outfit rather than wearing the hat on its own.

Before it was a television joke it was ordinary Ottoman headwear, standard for men in the late nineteenth century.