Lynette identifies the fungus as Horse Hoof Fungus which used to be used for tinder.
Apparently it can be boiled to remove all the protein, and leaves a felt like material, for which tinder was the main use, but the picture of a hat made from it shows its versatility!
Having said that, and read the details below ("liberated" from the internet, of course), the editor is not sure that he would wish to wear such a flammable hat!
Amadou is a Top Quality Natural Tinder with the following qualities:
Amadou is made from the Horse's Hoof Fungus (Fomes fomentarius), also known as Tinder Fungus and Hoof Fungus, and is one of the very best fire lighting tinder's around. Amadou is incredible natural tinder that has superior ember making properties with all spark, solar and fire piston based fire lighting techniques. Just a small pinch of this great tinder, about the size of your little fingernail, is sufficient to light a fire when using a properly prepared tinder bundle.