Season the pork loin generously with salt and pepper. Sear on all sides in hot oil in the Dutch oven until browned, then remove and set aside.
Add the onion, carrots, and potatoes to the pot, tossing briefly in the drippings.
Whisk the apple cider and mustard together and pour over the vegetables.
Nestle the pork loin back into the pot on top of the vegetables. Add the rosemary sprigs.
Cover and roast at 325°F for about 1½ hours, until the pork reaches an internal temperature of 145°F.
Rest the roast 10 minutes before slicing. Serve with the vegetables and pan juices spooned over.