In separate bowls, soak the bean thread noodles and wood ear mushrooms (fungus) in warm water for 15 minutes until they're fully reconstituted.
Drain the noodles in a colander and shake out the excess water. Coarsely chop the noodles into roughly 1 inch lengths.
Rinse the wood ear mushrooms, trim off the hard stems and thinly slice.
In a bowl, combine all the ingredients for the FILLING and mix well.
Trim about an inch off the ends of the bitter melons, then cut them in half crosswise.
Use a butter knife to carve and scrape out the seeds and white membrane of the bitter melons. Scrape along the inside to remove as much of the white membrane as possible. You should end up with hollow tubes of bitter melon.
Use a spoon or your fingers to stuff the bitter melons with the pork filling from one end to the other. Be sure to push out any air pockets. Use the butter knife to scrape the ends flat. Save any remaining pork mixture to add to the soup later.
Making the Soup
In a pot, combine chicken broth, fish sauce, soy sauce, salt and sugar and bring to a boil.
If you have any extra pork mixture, add it now. Break it up in the soup with a ladle.
Carefully add the stuffed bitter melons and allow the soup to return to a boil. Reduce the heat to medium-low, cover and simmer for 30-40 minutes, until the bitter melon is tender.
Use a fine mesh strainer to skim off any scum or impurities on the surface of the soup.
Slice the stuffed bitter melons into 1.5 inch thick pieces before serving.
Add additional salt to the Stuffed Bitter Melon Soup to taste.