Let the meat soak in a pot of cold water for 20 minutes. Rinse the bones off and pat dry with a paper towel.
Rinse out the pot, and then place over high heat. Once any residual water in the pot has dried off, add the oil to the pot, along with the ginger slices and the thicker white and light green parts of the scallions. Cook for 1 minute.
Add the lamb, and brown on all sides until lightly golden.
When the lamb is browned, add the water. Also add the garlic, green parts of the scallions, and the spices (dried chili peppers, cardamom pods, star anise, bay leaves, sand ginger, cinnamon, black cardamom, coriander seeds, sichuan peppercorns, white peppercorns, and fennel seeds).
Cover and simmer over medium-high heat for 30 minutes. Then reduce heat to medium, and simmer for 1 additional hour. The broth should turn cloudy and milky within the first 20 minutes of simmering.
Add the dried wood ears and salt, and cook for another 30 minutes over low heat, for a total of 2 hours of cooking.
When you’re ready to eat, boil the noodles per the package instructions. Transfer the lamb shanks to a cutting board. Debone them, and chop the meat roughly.
Serve each bowl with 2-3 ladlefuls of broth, poured through a fine-meshed strainer. Top with a healthy pinch or two of chopped Chinese celery leaves and cilantro, and serve with chili oil, Chinese black vinegar, and white pepper as optional condiments.