I found 2 very damaged straw hats in an op shop for very little a few years ago. They had a circular high crown with a circumference too small for my head.
I needed to make it larger, flat on top and oval. I pulled out all the thread and soaked the straw in hot water.
Once it was sewn I steamed it smooth and into the desired shape.
I then ran a single father stitch and tacked it just inside the edge of the brim.
As the silk is shedding bad I decided to bias tape the edge as leaving the top unlined will hopefully help with air flow when it is very hot.