My method was to use the directions from the C2C Moss Stitch Square,
I worked to the dimensions of The Clever Hat, testing to make sure it would stretch around my head. I made the rectangle approximately 25 cm by 43 cm, then did a stretchy Moss stitch along one long edge, which will be the turned up edge of the brim. Without even cutting the yarn, I did a crochet join of the two short edges, making it slightly stretchy, too. Again, without cutting yarn, I did a SC2Tog type stitch around and around on the crown to gather the top. Future versions might be made with a slightly wider short side. Perhaps 28 cm instead of 25 cm. That will give a little more room in the crown, and some flexibility for the depth of the brim.
It works, but there may be better ways to do it. I used Moss stitch because I thought it would have enough stretch for comfort.