I made a chef hat today for the dress up bin.
Here is the basic tutorial I followed in making my chef's hat. I did make a few adjustments.
I did not do the slit up the back or seal off the short ends of the head band. I simply pinned the band to the gathered circle and left a 3 inch gap of un-gathered circle between the ends of the bands. To finish off the band I inserted elastic into the ends, leaving the bands about 1/2" apart. This allows the hat to stretch to fit a slightly larger head.
I also made the top circle a bit bigger than the tutorial to give it more loft/floppyness. My fabric for this measured 20"x 20".
My band measurements: 1 piece of fabric cut to 6"x 20". Hem the 6" edges, then fold with right sides together to make a piece that is 3"x 20" Sew the 20" edge, then use a large safety pin to turn the right sides out. I used a pretty thick canvas like fabric. If I were to do it again I would not sew the 20" edge shut until I had pinned the length of the headband on either side of the gathered circle as I attached it, to create a nice, finished edge on both sides. Doing this could also make the hat reversible.