Add the beef shank, 3 slices of ginger, and 1 tablespoon Shaoxing wine to a large pot. Cover with cold water and bring to a boil. Drain, then rinse the beef thoroughly to remove any foam and impurities.
Clean the pot or use a separate clean pot. Heat the cooking oil over medium heat. Add the remaining ginger, garlic, and scallion whites and stir-fry until fragrant.
Return the beef to the pot. Add the soy sauce, dark soy sauce, Shaoxing wine, and oyster sauce. Stir until the beef is evenly coated in the seasonings.
Pour in enough water to just cover the beef, about 2 cups depending on the size of your pot. Add the dried chilies, cardamom, star anise, Sichuan peppercorns, and rock sugar.
Bring the liquid to a light boil. Taste the broth and add salt if needed.
Cover, reduce the heat to low, and gently simmer for about 2 hours, or until the beef is tender.
Add the daikon radish. Cover and continue cooking for 15–20 minutes, or until the radish is tender and has absorbed some of the braising liquid.
Garnish with chopped scallion greens and fresh red chili peppers. Serve hot with the braising liquid spooned over the beef and radish.