Perhaps you've noticed these thin, brown slivers of crunchy, squeaky mushrooms in hot and sour soup or in stir-fries. Called wood ear mushrooms, they're more easily found in dried form, but fresh ones can sometimes be found in Asian markets. And like their name states, they do grow on trees and they also look like ears!
This mushroom is also known as tree fungus, jelly fungus, Jew's Ear, and Judas' Ear. They're commonly found in Asian cuisine. They don't have a whole lot of flavor, but their squeaky texture is interesting. If purchased in dried form, simply reconstitute in some hot water. If bought fresh, rinse them under cold water to remove any dirt. Chop them up and add them to soups and stir-fries.
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(Image: Kathryn Hill)
Straw Mat from The ...

Those are beautiful things--look like velvety stuffed animals!
Your tip about slicing these up finely seems like a good one: I added them whole to a curry dish, and later to a stir-fry and the squidgy, gelatinous texture was a little much!
Hi:
It looks like you've photographed something that is *not* wood ear, but a lookalike that is not too closely related called: Exidia recisa
I've posted about them on: http://sites.google.com/site/foragingct/home/chef-s-tasting-table