Preheat the oven to 300 degrees F.
To begin, just throw the brown sugar, vinegar, olive oil, salt, dried oregano, cumin, chili powder, garlic and some pepper into a food processor or blender. (I happen to love brown sugar in my cooking, but you can decrease it or omit it if you like.) Cut 1 of the onions into quarters and put it in the food processor with the spices. Blend the ingredients until totally combined and then pour it over the pork shoulder. Now rub it into every nook and cranny of the meat, tucking it under folds and in crevices. Let no stone go unturned.
Cut the remaining 3 onions into wedges and make a bed of onions in a large Dutch oven. Place the pork on the onions and add a couple of cups of water. Cover tightly and roast until fork-tender, 6 to 7 hours, turning every hour. Crank up the heat to 400 degrees F, remove the lid and roast skin-side up for another 15 to 20 minutes to get the skin crispy. Let the pork rest for 15 minutes before shredding.
Shred the pork (2 forks work well) and put the meat into a pan or serving dish. Pour the juices and onions over the meat. Serve with lime wedges, sour cream, pico de gallo, tomatillo salsa ... whatever makes your skirt fly up!