Fill a large stockpot with cold water. Soak the short ribs in the water for 30 minutes to 1 hour to pull out impurities. Drain. Score ribs by slicing shallow criss-cross cuts across the meat.
Fill the stockpot with fresh water and bring it to a boil. Add the ribs and reduce heat to simmer; cook for 30 minutes. Drain the water from the pot. Add soy sauce, sesame oil, garlic, fresh and ground ginger, brown sugar, water, rice wine, pear and kiwi; season with salt and pepper. Bring to a boil, reduce to a simmer and cook 60 minutes.
Add carrot, potatoes, green and yellow onions and chestnuts and shiitakes if using. Simmer until vegetables are tender, at least another 30 minutes.