Preheat the oven to 450°F. Season the pork all over with a generous amount of salt and fresh ground pepper. Scatter the onion and carrot over the bottom of a roasting pan or large Dutch oven and place the pork, fat side up, on the vegetables.
Pour the apple cider around the pork and place in the oven, roasting for 45 minutes. Remove the pan from the oven and reduce the temperature to 300°F. Tightly cover the pan with aluminum foil (or a tight-fitting lid) and cook until the meat is tender and falls away from the bone, about 5 hours.
When the pork is cool enough to handle, remove the fat from the roast and shred the meat into bite-size pieces using two forks; discard the bone and large chunks of fat.
Shredded meat can be stored in airtight containers in the fridge for three days. To freeze it, portion the pork in 2-3 cup servings and freeze for up to three months.
To make pulled pork sandwiches, combine your favourite barbecue sauce and shredded pork in a medium saucepan set over medium-high heat and cook until warmed through. Serve on buns with a side of spicy coleslaw or a kid-friendly shredded veggie salad.
To make pork ragu, sauté one sliced onion and one minced garlic clove in some olive oil in a large saucepan, cooking until soft. Add 1 teaspoon fennel seeds, 1 (28 oz.) can crushed tomatoes, 1 cup red wine, ¼ cup Worcestershire sauce and 3 cups shredded pork. Stir well and simmer for a minimum of 30 minutes. Season well with salt and pepper and serve over pasta.
To make pulled pork tacos, heat some olive oil in a large skillet and sauté one chopped yellow onion and two minced garlic cloves, cooking until soft, about 10 minutes. Add 1 teaspoon ground cumin and 1 teaspoon chilli powder and stir well. Add 2 cups shredded pork and 1 teaspoon hot sauce (optional) and stir to combine, cooking until warmed through. Serve in tortillas with desired toppings.