Bring 4 cups of water to a boil. Add mushroom stems and onion. Cover and bring to a boil again, then simmer for about 1 hour, until water becomes cloudy and beige and onion is practically falling apart. Place your colander or strainer over a bowl, so you can pour the liquid into the bowl while the colander catches the mushrooms and onions.
Use a spatula or small bowl to press the excess liquid out of the mushrooms and onions, then discard. Add soy sauce to the resulting broth if desired (I like to do this to salt my broth slightly and give it a richer color). Use within 2 days or freeze.