Adjust the rack to the bottom third of the oven and preheat to 325 degrees F.
Add the chiles to a medium bowl and cover with the boiling water. Let steep for 20 minutes.
Sprinkle the short ribs generously on both sides with salt and pepper. Heat the olive oil in a large Dutch oven over medium-high heat until just under smoking hot. Add the short ribs in batches, leaving some room between each of them so they sear evenly, and cook until well browned, about 7 minutes per side (14 to 15 minutes per batch). Remove the short ribs to a platter in a single layer (no stacking) and repeat with the second batch.
Meanwhile, add the chile peppers with water, chicken stock, tomato paste, garlic, onions and a dash of salt to a blender, and mix until blended together.
Once the second batch of meat is seared, remove and set aside. Add the hard cider to the Dutch oven and scrape the brown bits left from the meat off the bottom of the pot. Pour the onion mixture into the pot and turn the heat up to high. Add the balsamic and rosemary sprigs and boil together for 2 to 3 minutes. Return the short ribs and any juice that may have accumulated on the platter back into the pot. Cover tightly with a lid and braise in the oven until the ribs are tender, about 2 1/2 hours.
Place the ribs on a platter covered with foil to keep warm. Put the Dutch oven on the stovetop over high heat and reduce the braising liquid until thick and saucy, 20 minutes. Add the ribs back to the pot before serving to coat with the reduced liquid. Place the ribs on plates and ladle the sauce over the top. Sprinkle with chopped parsley for garnish.