To make the sauce, combine the soy sauce, sesame oil, garlic, fresh ginger, ground ginger, brown sugar, water, rice wine, pear, kiwi, salt, and pepper in a large bowl. Whisk to combine.
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 clean water and bring to a boil. Simmer the short ribs in the water for 30 minutes. Drain. Return the simmered ribs to the pot; pour in the sauce, bring to a low boil. Simmer the ribs in the sauce for 60 minutes. Stir in the carrot, potatoes, green onions, yellow onion, chestnuts, and shiitake mushrooms. Simmer until vegetables are tender, at least 30 additional minutes.