Preheat the oven to 300°F (150°C).
Drain the beans, then rinse well under running tap water.
Transfer beans to an 8-quart pot or Dutch oven.
In a small bowl, thoroughly mix together the garlic, onion powder, fennel, salt, black pepper, paprika, cinnamon, and cayenne.
Rub the mixture all over the pork, then set the pork in the pot with the beans.
Add 4 ½ cups (1L) water along with the shiitake mushrooms, tomato paste, and fish sauce, stirring to ensure the tomato paste is completely dissolved.
Seal the pot with two layers of foil, crimped tightly around the edges to prevent any steam from escaping.
Cover with the lid, then transfer to the oven and cook until the pork is fork-tender and the beans have completely cooked through, about 4 hours.
Using a pair of kitchen tongs, remove and discard the shiitake mushrooms, then carefully transfer the pork to a large platter.
Using a pair of forks, shred the pork, then return it to the pot along with any juices on the plate.
Stir in the vinegar, then season with additional salt, if desired.
Garnish with cilantro or parsley and serve hot or warm with plain rice or toasted and buttered slices of sourdough bread.
Pork and beans garnished with greens.