Soak the beef short ribs in cold water for 1–2 hours, changing the water once or twice.
Boil the ribs for 3–5 minutes, then drain and rinse thoroughly.
Blend the apple, onion, mirin, and garlic until smooth.
Place the ribs in a pot and add all sauce ingredients.
Bring to a boil, then cover and simmer over low heat for 50–60 minutes.
Add the carrot and cook for 20 minutes, then add the mushrooms and cook for 10 minutes more.
Cook until the ribs are tender and the sauce has thickened slightly, then serve hot