Heat the oven to 350F degrees.
Rub the pieces of pork shoulder all over with salt.
With a dutch oven set the stovetop to medium-high and heat the oil. 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. Be careful of oil splatter.
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 to release all the tasty brown bits.
Add the pork back to the pan and add enough water so the pork pieces are 2/3rd’s submerged in liquid. Add the cinnamon sticks and stir in the chile powders, bay leaves, cumin, oregano, garlic, and onion.
Braise in the oven uncovered for 3 1/2 hours, turning the pork a few times during cooking, until much of the liquid is 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, discarding any obvious big chunks of fat.
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.