In a 3- to 4-quart pan over high heat, bring rice and 3 cups water to a boil. Reduce heat and simmer, covered, until rice is tender to bite, about 20 minutes.
Meanwhile, in an 8- to 10-quart pan or a 14-inch wok, set a rack over at least 1 inch boiling water. Choose a shallow, rimmed pan about 8 inches wide that fits on the rack and can be lifted out (fashion a string harness, if needed).
In the shallow pan, combine beef broth, 2 tablespoons soy sauce, sherry, black beans, ginger, garlic, brown sugar, chili flakes, and pork. Turn the meat over in the seasonings.
Cover pan with foil and set pork pan on rack; cover larger pan. Steam on high heat until pork is no longer pink in center (cut to test), about 12 minutes. Protecting hands, lift out pork pan and rack. Keep pork warm.
Add enough water to pan to make 1 inch deep and bring to a boil. Add bok choy, cover, and boil until just tender when pierced, 2 to 4 minutes. Drain.
Serve rice in bowls with pork and juice, and bok choy. Add soy to taste.