In a medium bowl, combine white/light green parts of scallions, lime juice, 1 tbsp soy sauce and 1/2 tsp sesame oil. Add steak, toss to coat and marinate for 10 minutes.
Bring a medium pot of water to a boil. Add noodles and edamame and cook for 8 to 10 minutes, until noodles are al dente. Meanwhile, in a small bowl, whisk vinegar, ginger, remaining 2 tbsp soy sauce and 1/2 tsp sesame oil and set aside. Drain noodles and edamame. Rinse with cool water until cold. Rinse pot with cool water until cold, then return noodles and edamame to pot. Add vinegar mixture and toss to combine.
In a large nonstick skillet, heat olive oil on medium-high. Transfer steak to skillet and discard marinade. Add peppers and sauté, stirring occasionally, until steak is cooked through, about 5 minutes.
Divide lettuce, noodle-edamame mixture and steak-pepper mixture among serving plates. Garnish with reserved dark green parts of scallions.