Rub the pieces of pork shoulder all over with salt. Refrigerate for 1 to 3 days. (You can skip this step if you want. Just be sure to salt the pork before searing the meat in the next step.)
Heat the oil in a roasting pan set on the stovetop. Cook the pieces of pork shoulder in a single layer until very well-browned, turning them as little as possible so they get nice and dark before flipping them around. If your cooking vessel is too small to cook them in a single layer, cook them in two batches. Do not crowd the pan or the meat won’t crisp up.
Once all the pork is browned, remove them from the pot and blot away any excess fat with a paper towel, then pour in about a cup of water, scraping the bottom of the pan with a flat-edged utensil to release all the tasty brown bits.
Heat the oven to 350ºF (180ºC) degrees.
Add the pork back to the pan and add enough water so the pork pieces are ⅔rd’s submerged in liquid. Add the cinnamon stick and stir in the chile powders, bay leaves, cumin and garlic.
Braise in the oven uncovered for 3½ hours, turning the pork a few times during cooking, until much of the liquid has evaporated and the pork is falling apart. Remove the pan from the oven and lift the pork pieces out of the liquid and set them on a platter.
Once the pork pieces are cool enough to handle, shred them into bite-sized pieces, about 2 inches (7 cm), discarding any obvious big chunks of fat if you wish.
Return the pork pieces back to the roasting pan and cook in the oven, turning occasionally, until the liquid has evaporated and the pork is crispy and caramelized. It will depend on how much liquid the pork gave off, and how crackly you want them.