Preheat the oven to 450ºF.
Season the pork with salt and pepper. Place in a medium roasting pan and add 1/2 cup of water. Place in the oven and roast for 1 hour. Reduce the heat to 350ºF and continue to cook for 3 hours. Remove from the oven and cool completely. In a large sauté pan, over medium heat, add the oil. When the oil is hot, add the onions. Season with salt and pepper. Sauté until the onions are caramelized, about 8 to 10 minutes, stirring constantly. Remove from the heat and cool completely. When the pork is cool, remove any excess fat and the bone. Shred the meat into bite-size pieces. In a mixing bowl, combine the pork, onions, chilies and cheese. Season with salt and pepper. Mix thoroughly.
Yield: about 3 1/2 cups