Place the pork in a large bowl and toss with the flour, salt, and pepper until coated on all sides.
Heat a Dutch oven or similar large soup pot over medium. Once hot, add 1 tablespoon of the oil and let warm about 30 seconds. Add half of the pork in a single layer (the pieces should barely touch). Let it cook undisturbed for 3 minutes until lightly browned on the first side, then flip and brown on the other side. Remove to a plate. Repeat with the remaining 1 tablespoon oil and remaining pork.
While the pork sears, chop the onion into 1/2-inch pieces.
Once all of the pork is browned and removed to a plate, reduce the heat to medium-low. Add the onion and cook, stirring periodically and scraping the bottom, until softened and browned at the edges, about 10 minutes.
While the onion browns, peel the apple and grate on a coarse box grater. Smash the garlic, then peel and roughly chop.
Once the onions are browned, stir in the garlic and apple and cook just until fragrant, about 30 seconds.
Add the hard cider and apple cider vinegar and bring to a simmer. With a rubber spatula or wooden spoon, scrape up any bits stuck to the bottom of the pot. Let simmer 2 minutes to reduce slightly.
Return the pork and any juices that have collected on the plate to the pot. Stir in the chicken broth, Worcestershire, sage, bay leaves, and cinnamon stick. Bring to a boil over high heat, then reduce to a simmer over low. Cover, leaving the lid just slightly ajar, and simmer for 90 minutes. Lift the lid and stir periodically to ensure nothing is sticking. The liquid will noticeably reduce.
While the pork simmers, peel the carrots, parsnips, and potatoes. Cut each into 1/2-inch cubes. Once the pork has been simmering 90 minutes, stir them in. Cover the pot partway and simmer 45 minutes to 1 hour more, until the vegetables are tender. Stir from time to time to prevent sticking, and if at any point the stew is thicker than you would like, add water as needed (I added about a cup but it's also VERY dry where I live).
Fish out and discard the bay leaves and cinnamon stick. Stir in the Dijon and let cook 2 minutes. With a potato masher, lightly mash the stew a bit. This will break up a few of the potatoes to slightly thicken the broth and also give you smaller bits of pork mixed in with the larger. Taste and adjust the salt, pepper, and mustard as desired. Serve hot with parsley or sage sprinkled over the top.
Notes
TO STORE: Refrigerate leftover pork stew in an airtight container for up to 4 days. I don't recommend freezing this recipe; potatoes tend to get mealy after freezing and thawing.
TO REHEAT: Warm gently on the stovetop over medium-low heat, stirring occasionally. Add a splash of broth or water if it has thickened in the refrigerator.
Because regular apple cider is sweeter than dry hard cider, I'd start with a mixture of 3/4 cup apple cider and 3/4 cup additional chicken broth in place of the 1 1/2 cups hard cider. Taste the finished stew and add a little extra apple cider vinegar or Dijon if it needs more acidity.