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Step 1
Preheat the oven to 325 degrees.
Step 2
Trim the pork shoulder of any thick layers of fat. Combine the brown sugar, cumin, paprika, salt, and pepper in a small bowl. Rub the pork with the spice mixture, getting into crevices and on the sides. Allow the pork to sit for about 30 minutes.
Step 3
Heat the olive oil in a large dutch oven over medium-high heat. Brown the pork on all sides, about 3 minutes per side. Remove from the pot. Add the onions, carrots, garlic, tomatoes, and beer. Bring to a simmer, scraping the bottom of the pot with a wooden spoon to bring up any browned bits.
Step 4
Return the pork to the pot. Cover and put in the oven for 3 1/2 to 4 hours, checking once or twice, until the meat is extremely tender and pulls away from the bone easily. Shred the pork in the pot, using tongs to separate the meat from the fat (see photos above). Discard the bone or set aside for another use.
Step 5
Serve the meat with several spoonfuls of the vegetables and sauce.