Assemble, prepare, and measure ingredients. Chop onions. Grate ginger. Slice mushrooms. Slice garlic. Preheat oven to 275°F/135°C.
Warm 2 tablespoons of olive oil in a cast iron or enameledcast iron Dutch oven, or other oven-safe pan with a lid, over medium-high heat. Season short ribs with salt and pepper and sear on all sides until deep brown, 15–20 minutes in total. Remove from pan and set aside, leaving residual oil in pan.
Add onions, ginger, mushrooms, and garlic to hot oil in pan and sauté for 5–7 minutes, or until onions are translucent. Add star anise, Szechuan pepper, and cardamom. Cook for 30 seconds, stirring constantly. Return short ribs to pan. Stir in tamari and then add just enough beef stock to come up the sides of the meat but not to cover it (you may not need the full 2 cups/500 mL). Cover and braise in oven for 3½–4 hours, until meat is falling off the bone.
Transfer ribs to a bowl, pull out and discard bones, and separate meat using two forks. Skim off and discard liquid fat from surface of braising liquid. Bring liquid to a boil over high heat for 8–10 minutes, or until it has thickened and is intensely flavorful. Remove star anise from sauce.
Serve short ribs with some of their delicious sauce over top and extra on the side.