Combine the soy sauce and shrimp; cover and refrigerate 30 minutes. Drain through a sieve over a bowl, reserving soy sauce.
Prepare noodles according to package directions, omitting the salt and fat. Drain and rinse; drain well. Toss noodles with 1 teaspoon oil. Set aside.
Heat 2 teaspoons peanut oil in a large nonstick skillet over medium-high heat. Add onion; stir-fry 3 minutes. Add broccoli and bell pepper; stir-fry 3 minutes. Add garlic and ginger; cook 1 minute, stirring constantly. Remove vegetable mixture from pan.
Heat 1 1/2 teaspoons peanut oil in pan. Add shrimp, and stir-fry 1 minute. Add the reserved soy sauce, broth, and salt, and bring to a boil. Add noodles, vegetable mixture, and nuts, and toss well to combine.