Preheat the oven at 350F. Place the rack on the lower part of the oven.
Trim all the fat from the pork shoulder and cut into 1-inch cubes. In a large cast enamel pot, over medium high, heat the olive oil. Add half of the pork cubes, do not overcrowd the pot, sear for a couple of minutes. Remove the meat from the pan and place on a plate. Add the remaining pork shoulder to the pan and sear for about a couple of minutes. Remove from the pot and add with the first batch.
Add the wine and vinegar to the pot and scrape any bits that may have stuck to the bottom or sides. Add the onions, carrots, garlic and ginger. Lower the heat to medium and cook for about 5 minutes, stirring occasionally, until the onions are soft.
Add the pork shoulder back to the pot over the onion’s carrots mixture. Season with salt and pepper. Add lime juice and fresh thyme. Stir all. Add the chicken broth to slightly cover the pork. (you may have some stock left over)
Cover with a tight lid and place in the hot oven. Cook for about 2 to 2 ½ hours, covered and stirring once in a while.