This recipe is meant to be a guide: you can add different liquids, vegetables, and seasonings - it's a very forgiving recipe. If you'd like to use a slow cooker instead of a Dutch oven, be sure to reduce the liquid so that it doesn't boil over.
Trim the pork shoulder of any thick layers of fat. In a small bowl, mix together the brown sugar, cumin, paprika, salt, and pepper. Rub the pork all over, including crevices, with the spice mixture. Allow to rest for 30 minutes.
Heat the olive oil in a large Dutch oven over mudium-high heat. Add the pork, and brown it on all sides, about 3 minutes per side. Transfer to a plate. Add carrots, onions, garlic, tomatoes, and beer to the Dutch oven. Simmer over medium-high heat, using a wooden spoon occasionally to scrape up any browned bits. Return the pork shoulder to the pot and cover. Cook in the oven for 3 1/2 - 4 hours, until the meat is very tender and pulls easily away from the bone. Use tongs to shred the pork.
Serve the pork with the sauce spooned on top, alongside the vegetables.