Set a large nonstick skillet or wok over medium-high heat.
Add the pork and 1 tablespoon of the soy sauce and cook, using a wooden spoon to break the meat into small pieces as it browns, about 3 minutes.
Add the onion, garlic, and ginger and cook, stirring, until the vegetables are soft, 2 to 3 minutes. Add the cabbage, bok choy, carrots, and mushrooms.
Pour in the remaining 2 ½ tablespoons soy sauce, the rice wine, and sesame oil.
Cook, stirring occasionally, until the cabbage and bok choy are wilted but still crunchy, 3 to 4 minutes. Serve hot, garnished with scallions.
