Turn the broiler on high. Brush your peppers in olive oil on all sides and arrange on a rimmed cookie sheet. Roast under the heat until the skin begins to blister, turning peppers as necessary so they roast evenly. This should take between 4-7 minutes per side. Once your pepper skins have blistered, place in a bowl and set aside.
Preheat the oven to 275°F. Generously season the pork on all sides with salt. Heat a dutch oven over medium-high heat until drops of water quickly evaporate. Add pork shoulder, fattiest side down, and sear 5-8 minutes per side, or until deeply golden brown. Turn heat to medium-low and set the browned pork butt aside.
Cut the head of garlic in half horizontally and sear the exposed garlic cloves in the rendered pork fat until a nice caramel color, lowering heat if necessary. Remove from heat and add the onions. Sear undisturbed until the onion quarters take on some color, about 3 minutes.
Add stock and vinegar to the pan, scraping up any flavorful browned bits from the bottom of the dutch oven. Season the liquid with salt and pepper. Settle the pork butt into the liquid, fat side up, and add the two halves of the seared garlic head, bay leaf, rosemary, and thyme. Bring the mixture to a boil, then turn off the heat. Cover, then place in the oven for 3.5-4 hours, or until pork is falling off the shoulder bone.
Pull pork out of the liquid using tongs and, once it has cooled slightly, break apart using a fork or gloved hands. If necessary, cut any long muscle fibers against the grain to enhance tenderness.
Gently pull peppers from the cooking liquid and remove seeds and stems. If desired, roughly chop into bite sized chunks. Using tongs, place pork, peppers, corn, and cilantro into a warm tortilla and squeeze lime over the top. Serve immediately. Pork keeps up to 5 days in the fridge.