Combine broth, oyster sauce, honey, ginger and cayenne pepper in large saucepan; bring to boil. Cover and reduce heat to low.
Bring 4 quarts water to a boil. Add noodles. Boil for 4 minutes until tender, stirring occasionally. Drain and rinse. Divide noodles among 6 soup bowls.
Heat a 12-inch skillet over high heat. Add 2 tablespoons peanut oil, then the chicken, spreading evenly. Cook without stirring 20 seconds; then stir-fry chicken until no longer pink, about 2 minutes. Stir in rice wine and soy sauce. Transfer to plate.
Add remaining 1 tablespoon oil to same pan over high heat. Add cabbage, carrot, and sugar. Stir-fry 30 seconds. Stir in chicken and any juices. Stir-fry 1 minute. Top noodles with chicken mixture. Ladle hot broth among bowls. Serve immediately and enjoy!