Put the rack in the middle of the oven and preheat the oven to 175°C/350°F/Gas 3.
Place the meat in a shallow, 3-litre (5 pt) baking dish. Generously season the meat on all sides with salt. Pour the Chile Colorado Sauce over the meat and rub it on all sides of the meat. Cover the dish tightly with two layers of foil and cook in the oven until the meat is very tender, about 3 to 3½ hours.
Remove the dish from the oven (keep the oven on), remove and reserve the foil, and let the meat cool in its liquid, about 30 minutes.
Coarsely shred the meat with your fingers or by using two forks, discarding the bones. Return the meat to the cooking liquid, stir, cover the dish again with the foil, and return it in the oven until the sauce is hot, about 30 minutes.
After about 15 minutes, make two stacks of tortillas, wrap the stacks in foil, and put them in the oven to heat.
Serve the meat in the baking dish with the tortillas and other accompaniments in bowls alongside, and let everyone assemble their own tacos at the table.
Locally grown New Mexico chili peppers are a sacred crop in the Southwest. They add a zesty bite to dishes like burritos, cheeseburgers and even chocolate.