1. 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.
2. 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).
3. In the shallow pan, combine vegetable broth, sherry, soy sauce, black beans, ginger, garlic, brown sugar, and chili flakes. Drain tofu on towels and cut into 1/2- by 1 1/2-inch pieces. Turn tofu over in seasonings in pan.
4. Cover pan with foil and set tofu pan on rack; cover larger pan. Steam on high heat until tofu is hot, about 10 minutes. Protecting hands, lift out tofu pan and rack. Keep tofu warm.
5. Add enough water to pan to make 1 inch deep and bring to a boil. Add broccoli, cover, and boil until just tender when pierced, 2 to 4 minutes. Drain.
6. Serve rice in bowls with tofu and juice, and broccoli. Add soy to taste.