Chaperon

The chaperon began as a sort of hood, though more decorated and larger.  It had leaf-like edges at the bottom, and the hood had a long point called a liripipe.
In the early 1300s, someone with either no taste in fashion or as a joke wore a chaperon with his head stuck through the face opening rather than through the bottom.  Strangely, this odd-looking style caught on.  The liripipe was lengthened even further to counterbalance the weight of the other side.
After a while, the liripipe was thrown away entirely, and the chaperon was made into more of a hat, its base being a stiffened band.  It was popular in Italy during the Renaissance.
Trade with the Middle East influenced the chaperon quite heavily, and it gained a turban-like appearance.  The roll that was its base became padded until it looked like a fat donut.

For more information:

bullet Chaperons and how to make them