Pre-heat the oven to 325°F. Season the pork generously with salt and pepper and let sit at room temperature for 30 minutes.
Pat the pork dry with a paper towel. Heat a large Dutch oven or heavy-bottomed pot over medium-high heat with the EVOO, three turns of the pan. Place the pork in the pot and sear it all over, about 4-5 minutes per side, or until golden brown. Remove the pork, set on a plate and reserve.
Turn the heat down to medium, then add the onion and garlic and cook for 5 minutes. Season with cumin, oregano, salt and pepper. Deglaze the pot with the beer, scraping up the bits stuck to the bottom of the pot. Add the chicken stock and orange juice and stir. Add the reserved pork back to the pot (the liquid should come 2/3 the way up the meat) and bring to a simmer. Cover and place in the oven for 2 1/2-3 hours, turning the meat halfway through cooking, until the meat is tender and falls apart when you touch it. Remove the pork from the pot, place it on a plate and tent with foil to keep warm. When the pork is cool enough to handle, pull the meat apart with two forks.
Simmer the braising liquid over medium heat until it’s reduced by half. Add the lime juice and set the shredded pork into the liquid.
While the pork is cooking, prepare the pickled red onions: In a small saucepot, bring the white wine vinegar, sugar, 1 teaspoon salt, chili pepper and bay leaves to a simmer. Place the sliced red onions in a small sealable container. Carefully pour the hot liquid over the onions, cover and give it a shake. You may need to lift the lid to release some of the pressure. Every now and then, give it a good shake. Place in the fridge to cool.
To assemble, using tongs, remove the pork from the liquid and place on the rolls. Top with a few pickled jalapeños, some pickled red onions and some crumbles of cheese and top with the roll tops.