1. Rinse chicken and pat dry. Cut crosswise into strips about 1/8 inch thick and 2 to 3 inches long. In a bowl, mix chicken with sherry. In another small bowl, mix broth, soy sauce, cornstarch, and white pepper.
2. Remove and discard any yellow, damaged, or tough leaves from 1 pound Asian greens. Trim off and discard tough stem ends. For tough stalks, remove any thick side stems attached to center stalk; discard center stalk and use stems. Rinse well.
For bok choy: Cut leaves and stalks diagonally or crosswise into 1/4-inch-thick slices; separate leaves from stalks.
For Chinese mustard or yao choy: Trim stalk ends, especially if fibrous (a white, woody center is an indication). If skin on stalks is tough, peel off and discard. Cut greens into 3-inch lengths, separating leaves and thin stems from thicker stems or stalks. If any pieces are thicker than 1/2 inch, cut to that thickness.
3. Set a 14- to 16-inch wok or 12-inch frying pan over high heat. When hot, stir in the thick stem pieces and 3 tablespoons water. Cover and cook until pieces are tender-crisp to bite, 2 to 3 minutes. Add the leaves and thin stems and stir until leaves are barely wilted, 1 to 2 minutes; pour mixture into a bowl.
4. Return pan to high heat. When it's hot and any liquid has evaporated, add oil, garlic, and ginger; stir until garlic begins to brown, about 30 seconds. Add chicken and stir until no longer pink in the center (cut to test), 2 to 3 minutes. Stir broth mixture and add to pan; stir until boiling. Return greens to pan and stir until hot. Add salt to taste and pour into a serving bowl.