Generously salt and pepper the pork shoulder; let meat come to room temperature, about 2 hours.
Preheat oven to 325 degrees F.
Add olive oil to a large ovenproof pan. Sear the pork over medium-high heat until very brown on all sides. Remove pork from the pan; let rest on a platter for 10 to 15 minutes.
Leaving an even coating, drain excess oil from the pan. Add onions; sweat over low heat until translucent. Return pork to the pan; add remaining ingredients. Cover pan, place in the oven and cook for 2 to 3 hours or until the internal temperature reaches 140 to 150 degrees F. Let pork rest 10 to 15 minutes before slicing.
Use as burrito/taco meat or you can serve with vegetables and potatoes.