How to Make It
In a medium bowl, cover the shiitakes with the boiling water and top with a heatproof plate to keep them submerged. Let stand until they are softened, about 25 minutes. Using a slotted spoon, transfer the shiitakes to a work surface and cut in half. Reserve the soaking liquid.
In a large saucepan, heat the oil. Add the king oyster mushrooms, shallots and a generous pinch of salt and cook over moderately high heat until just starting to soften, about 3 minutes. Stir in the shiitakes, garlic, star anise and five-spice. Add the wine and simmer until evaporated, about 2 minutes.
Add the shiitake soaking liquid to the saucepan and bring to a boil. Simmer over moderate heat, stirring occasionally, until the soaking liquid is slightly reduced, about 10 minutes. Add the mustard greens and cook, stirring occasionally, until just tender, about 5 minutes. Discard the star anise. Season with salt and pepper. Serve.