Look for the noodles and sesame oil in the Asian foods section of the supermarket. Save time by using bottled ground ginger instead of fresh.
Heat oil in a large nonstick skillet over medium-high heat. Add mushroom, chopped onion, and carrot; sauté 3 minutes. Add ginger; sauté 1 minute. Stir in hoisin and 1 tablespoon soy sauce. Add broth and noodles; bring to a boil. Cover, reduce heat, and simmer 8 minutes or until noodles are done, stirring frequently. Place cabbage and turkey in a large bowl. Add noodle mixture to turkey mixture; toss gently to coat. Stir in remaining 1 tablespoon soy sauce and green onions.