Soak the short ribs in cold water for 1 to 2 hours, changing the water once or twice, to draw out surface blood.
Bring a pot of water to a boil and parboil the ribs for 5 minutes. Drain, rinse under cold water, and trim any large surface fat.
Whisk the grated pear, soy sauce, sugar, rice wine, garlic, ginger and black pepper into a marinade. Toss the ribs in it and let them sit 30 minutes (only 15 if using kiwi).
Transfer the ribs and marinade to a heavy pot, add the water or stock, and bring to a boil. Skim off any foam that rises.
Reduce to a low simmer, cover, and cook 45 minutes, skimming fat from the surface occasionally.
Add the radish and carrot. Cover and continue simmering 30 more minutes.
Add the potato, jujubes and chestnuts (if using). Cover and simmer 20 to 25 more minutes, until a fork slides through the meat with almost no resistance.
Add the onion, then uncover the pot for the final 15 to 20 minutes, stirring occasionally, letting the sauce reduce to a thick, glossy coating rather than a pool.
Drizzle with sesame oil and scatter scallions and pine nuts over the top before serving.