Place picnic shoulder in a large pot or Dutch oven. Whisk remaining ingredients together and pour over shoulder. Cover and bring to a simmer on the stove. Place, covered, in oven and cook for about 3 hours, basting often and turning meat over after 90 minutes, until meat yields easily when a fork is inserted.
Lift pork shoulder to a cutting board. Peel away skin from shoulder, scrape away any excess fat and discard. Skim off fat from top of juices in pot. With 2 forks, pull pork into shreds and toss with juices. Reheat on the stove and serve on a bun or over cooked rice.