World's Simplest Hat Pattern?

 Maybe! 

 It's The Egg Hat by Center For Pattern Design and is described:

"The bias-cut Egg Hat is inspired by Madeleine Vionnet's approach to pattern design. It is a simple, clean design which is easy to assemble and yet delivers a timeless elegance typical of her manner."

At the moment, the website seems to be undergoing some restructuring and not all patterns are shown, so here's a peek:

I had a large scrap of navy felted wool so I thought I'd (finally) give it a try -- the pattern has been living in the pattern stash for several years. As it happens, that was not a great choice in fabric for two reasons.  One, the felted wool, even cut on the bias, had zero stretch. (Duh!) But more importantly, it also rubbed off navy dye all over my hands when working with it.  Nope -- I may be a granny, but I can do without blue hair, thank you very much! It's funny, I never noticed that problem when cutting a vest out of the rest of the fabric, but I suspect there was a lot more handling of the fabric with the hat.  At any rate, there's a cut out vest I won't be finishing.

There is only one pattern piece -- an ellipse -- that is cut out twice.  Looks like this:

Sewn right sides together, then turned and folded in on itself, like so:

Scootch up one side into soft pleats and either secure the pleats with stitches, or as I did -- with a pin.  Done!

And a side view:  

While this one will end up as a test model, I do intend to make up another one -- next time in something that will have a bit of stretch, as this one was just too tight for comfort.