1. In a medium pan over high heat, bring chicken broth to a boil. Add rice noodles, stir to submerge, and remove from heat. Let soak until tender to bite, about 15 minutes. Pour noodles into a colander set over a bowl to drain; reserve broth.
2. Meanwhile, set a 10-inch nonstick frying pan over medium-high heat and add 1 teaspoon oil; when hot, pour in egg and swirl to make a paper-thin pancake. Cook until set, about 1 minute. Slide pancake from pan onto a board and let cool, then cut into thin strips.
3. In a small bowl, mix chicken with noodle soup base and rice wine. Pour 2 tablespoons oil into a 14-inch wok or 12-inch frying pan (with at least 2 1/2-in.-tall sides) over high heat. When hot, add chicken mixture and stir until no longer pink in the center, about 45 seconds. Add carrots and stir until tender-crisp to bite, 1 to 2 minutes. Add mushrooms and stir until beginning to brown but still firm to bite, 45 seconds to 1 minute. Add cabbage and stir until barely wilted, about 30 seconds longer. Pour chicken and vegetables into a bowl.
4. Reduce heat to medium-high, add remaining 2 tablespoons oil to wok, and pour in softened noodles. Stir vigorously to separate, then cook until heated through, 2 to 3 minutes. Add chicken-vegetable mixture and stir until heated through and mixed well, adding a little of the reserved chicken broth if mixture seems too dry; reserve remaining broth for other uses. Stir in salt to taste. Pour noodles into a serving dish and top with strips of egg.
Note: Nutritional analysis is per serving.