Preheat the oven to 325°F (165°C) and move the oven rack to the lower-middle position.
Pat the 3 pounds boneless pork shoulder dry with paper towels and season with 1 teaspoon kosher salt and ½ teaspoon freshly ground black pepper.
Heat 2 tablespoons olive oil in a large dutch oven over medium-high heat.
Working in batches, add the pork to the pot and sear on all sides, turning with tongs, 2 to 3 minutes per side. Remove the seared meat to a bowl.
Reduce the heat to medium and pour off all but 2 tablespoons of fat from the pot. Add the 1 large yellow onion and saute until softened, about 5 minutes.
Stir in the 2 garlic cloves, 1 teaspoon dried sage, 1 teaspoon dried thyme, 1 teaspoon ground mustard, ½ teaspoon ground nutmeg, and ¼ teaspoon ground cayenne pepper. Cook until fragrant, stirring continuously, about 1 minute.
Add the pork and any juices in the bowl back into the dutch oven.
Add the 4 cups low-sodium chicken broth or stock and 1 cup dry hard apple cider. Bring to a boil scraping any additional brown bits from the bottom of the pan, cover, and place in the oven to braise for 2 hours.
Remove the pot from the oven and add the 3 tablespoons apple cider vinegar, ½ pound sweet potatoes (1 large), 1 pound kohlrabi (2 medium), and 2 medium firm sweet apples. Cover and place back in the oven for thirty more minutes. Remove the pot from the oven again and add the 1 cup green beans Cover and place back in the oven and cook for an additional 30 minutes until the vegetables are tender.
Taste and season with salt and pepper as needed.
Slow Cooker
Pat the 3 pounds boneless pork shoulder dry with paper towels and season with 1 teaspoon kosher salt and ½ teaspoon freshly ground black pepper.
Heat 2 tablespoons olive oil in a large Dutch oven over medium-high heat.
Working in batches, add the pork to the pot and sear on all sides, turning with tongs, 2 to 3 minutes per side. Remove the seared meat to a bowl.
Place the 1 pound kohlrabi (2 medium)½ pound sweet potatoes (1 large), 2 medium firm sweet apples, 1 cup green beans, and 1 large yellow onion in the bottom of a slow cooker. Add the pork, 2 garlic cloves, 1 teaspoon dried sage, 1 teaspoon dried thyme, 1 teaspoon ground mustard, ½ teaspoon ground nutmeg, ¼ teaspoon ground cayenne pepper, 4 cups low-sodium chicken broth or stock, 1 cup dry hard apple cider, and 3 tablespoons apple cider vinegar.
Cover and cook on LOW for 6-8 hours or on HIGH for 3-4 hours until the meat and vegetables are tender.
Taste and season with salt and pepper as needed.
Notes
I don't recommend substituting pork tenderloin or pork chops. They are typically too lean and will dry out during the long braising time. Pork loin and pork chops are better saved for dishes with a shorter cooking time. Salt and pepper the meat about 30 minutes before cooking to maximize flavor. This will allow the salt to permeate into the meat flavoring it throughout. It will also help dry out the surface of the meat ensuring a great sear.Brown the pork in batches. Crowding the pan by trying to brown all of the meat at once will cause it to steam instead of sear. Preventing the meat from browning and developing a lovely caramelized flavor.Kohlrabi: Sometimes kohlrabi can be difficult to find at the store. If you can't find any kohlrabi turnips make a great substitute.Save the kohlrabi leaves and saute them like kale or other leafy green vegetables.You could substitute fresh herbs for dried herbs but you will need to double the amount.Hard Apple Cider: If you are avoiding alcohol try substituting regular apple cider. You could also substitute a semi-dry white wine.Storage: Place leftovers in an airtight container in the fridge for up to 1 week. To reheat, place the leftovers in a pot on the stovetop and cook over medium heat until warm.Freezer: Place in an airtight container, label with the contents and date, and store in the freezer for up to 3 months. The stew can be reheated from frozen in the microwave or a pot on the stove.