In a one-gallon resealable bag, combine soy sauce, brown sugar, lime juice, and ginger. Add steak; seal and toss until well coated. Allow to marinate for at least 15 minutes or up 2 hours in the refrigerator, turning frequently.
In mixing bowl, toss broccoli florets with olive oil.
Skewer steak and broccoli. Sprinkle kebabs with black pepper.
Preheat an outdoor grill to medium-high
Grill kebabs, turning occasionally, until steak is medium, about 8 minutes.
Squeeze with lime, garnish with scallions, and serve.