You will need a remnant of 4-way stretch fabric and matching thread. Polyester/spandex blend makes a nice sleepy hat. Brushed rayon blend is cozy for outdoor winter activities. I think this would also work if you were careful to horizontally orient the stretch of a 2-way fleece. But this is South Florida and that's theoretical.
Step 1: Cut & Pin
A 5 quart bowl was just right for cutting a hemispheric pattern. Then pin the cut edges.