1. Cook noodles according to package directions. During last 2 minutes of cooking, add spinach to same pot; cover and cook just until wilted. Drain and toss in a bowl with the sesame oil and salt. Divide noodles and spinach among 4 serving bowls; keep warm.
2. Rub grated ginger and chopped garlic over salmon.
3. Combine broth, anise, garlic slices, ginger slices, sake, soy sauce, and pepper flakes in a deep 12-inch-wide skillet. Add salmon and bring to a simmer. Cover and simmer 4 to 5 minutes; let stand 2 minutes. Transfer salmon to bowls with noodles and spinach. Remove star anise, garlic and ginger slices from broth. Ladle hot broth into bowls. Sprinkle with green onions.