For the black bean sauce: Put the black beans, rice wine, soy sauce, garlic and chile in a food processor and blitz briefly; be careful not to puree into a smooth sauce.
For the stir-fry: Slice the bok choy stems.
Heat a wok over high heat and add the vegetable oil. When the oil begins to smoke, add the bok choy stems and mushrooms. Stir-fry for 1 minute, then add the leaves of the bok choy. Stir-fry for 1 minute more.
Add the black bean sauce and gently stir to coat all of the ingredients.
Add the hot stock and bring to a boil. Season with the soy sauce and stir in the cornstarch and water mixture. Cook for 1 minute or less to thicken the sauce.
Serve immediately garnished with sliced scallions.