In a mortar or food processor, place the oregano, thyme, garlic and black peppercorns. Use a pestle to mash the ingredients into a paste. Once a smooth paste is formed, add the olive oil little by little to the mortar and set aside. Rinse the pork shoulder under cold running water and pat dry. Use a sharp paring knife to score the skin about 1/4-inch deep in a cross hatch pattern all over the thick skin of the pork roast. Season with 2 tablespoons of the kosher salt and rub well. Rub the entire roast well all over on all sides with the paste from the mortar and pestle. Place the pork in a plastic oven bag and add 1 cup of the sour orange juice over it. Seal the bag and force out as much air as possible, then place in the refrigerator for at least 8 hours, and up to 24 hours. Be sure to turn the bag over once or twice to redistribute the sour orange juice.
The next day, preheat the oven to 350 degrees F. Be sure to pull out the pork at least 1 hour and up to 4 hours before roasting. Place the pork in a roasting pan and season with the remaining 2 tablespoons of kosher salt. Wrap the roasting pan with aluminum foil and place in the oven. Roast the pork for 1 hour before turning the oven down to 275 degrees F. Continue to roast the pork for 3 more hours. Remove the foil and baste the roast with the remaining cup of sour orange juice. Roast for 1 additional hour and remove from the oven.
To fry the plantains, set a 10-inch saute pan over medium heat and add the vegetable oil. Once the oil is hot, add the plantains to the pan and fry in batches until golden brown, about 2 minutes per side. Remove from the pan, drain on a paper-lined plate, and season with salt. Serve while hot, with the Cilantro Crema on top, pork and Rice and Beans on the side.
Combine the heavy cream and buttermilk in a glass bowl or jar with a lid and stir or shake well to blend thoroughly. Allow to sit in a warm place, unrefrigerated, until cream is thickened and somewhat set, up to 6 hours. Shake well and refrigerate overnight before using. When ready to serve, add cilantro, lime juice and salt and pepper.
Rice and Beans:
Put the black beans and bay leaves in a large pot, cover with 3 quarts of cold water, and place over medium heat. Cover and cook the beans until tender, about 45 minutes to 1 hour. Check the water periodically; add more, if necessary, to keep the beans covered. Drain the beans and reserve 4 1/2 cups of the cooking liquid (if you do not have enough cooking liquid, use water to bring the liquid volume up to 4 1/2 cups).
Preheat the oven to 350 degrees F.
Coat a large Dutch oven or other ovenproof pot with the olive oil and place over medium heat. When the oil begins to smoke, add the salt pork and cook until most of the fat has rendered, about 2 to 3 minutes. Add the onion, garlic, and peppers and cook, stirring often, until the vegetables are softened, about 8 minutes. Do not allow to brown. Add the chicken broth and continue to cook until the liquid is evaporated, about 3 to 4 minutes. Add the cumin, coriander, and black pepper and stir to combine. Add the rice and cook, stirring, until lightly toasted, 4 to 5 minutes. Add the cooked black beans to the pan along with the reserved bean cooking liquid, lime juice and salt; stir to combine. Bring to a boil, cover, and transfer the pan to the oven. Bake until the rice has absorbed all the liquid and is cooked through, 25 to 30 minutes. Remove from the oven and let sit for 5 minutes before removing the lid and serving.