Preheat the oven to 400°F.
Toss the broccoli with oil, salt and pepper on a baking sheet and roast for 12 minutes, until crisp-tender.
Bring a large pot of salted water to a boil. Add the noodles and cook according to package instructions. Drain, return to the pot and toss with sesame oil.
Whisk the vinaigrette ingredients together in a large bowl. Add the noodles, carrots, cabbage and green pepper. Toss to coat.
Dry the steaks and season with salt and pepper.
Heat a large skillet or grill over high heat. Add the steaks and sear each side for 1-2 minutes, then move to a cooler part of the grill or pan and cook to your desired doneness (135°F for medium-rare, 125°F for rare). Rest for 5 minutes before slicing on the diagonal.
To serve, divide the noodles and broccoli between plates. Top with steak and garnish with peanuts, cilantro and lime wedges.