Pat Johnson did a miniature hat demonstration for our club a few months ago. It was quite an exciting demo!
First thing is that he turns these from woods like Cherry, Maple, or Holly. They are good woods for this application. I'm not sure exactly why, but I think they don't crack as easily as some other woods.
The other thing is that he turns them while they are soaking wet. He tries to cut the blank from the tree the day he turns them and then keeps them in a bucket of water til he's ready to turn them.
This also ensures that his light will shine through the wood on all the different steps so that he can maintain a consistent thickness. He even has a light that he can put in the headstock spindle to shine up inside the hat so as to get a consistent thickness in his last cut. (At this point we're all sitting on the edge of our seats!)
He also turns them to 3/32 of an inch thickness which curtails most cracking since all the wood dries at a consistent rate.
Since this thin wood is spinning all the water out, it begins to get dry too soon, so he also keeps a spray bottle on hand to keep it wet.
Pat used a clamping form to clamp the main body of the hat to an oval form while it dried. This same clamp is used in conjunction with large rubber bands wrapped around the brim to slowly bend it while it dried.
It's quite an interesting project. I've not been brave enough to even attempt it. I'm still working up to a bigger bowl... 🙄