Slice the beef against the grain into 1/2-inch wide strips and place into a large resealable bag. In a bowl, whisk together the soy sauce, oil, lime juice, brown sugar, garlic and ginger.
Pour the marinade into the bag over the beef. Seal the bag and toss to coat completely. Place the bag into a large bowl and put into the refrigerator to marinate for at least 1 hour or as long as overnight.
Preheat a grill or grill pan over medium-high heat. Thread 12 of the beef strips onto the skewers. Oil the grill gates and place the beef on the grill. If desired, reserve the remaining beef strips and marinade for another use, such as Round 2 Recipe Beef and Cabbage Stir Fry. Cook the skewers 2 to 3 minute per side.
Remove from the heat, place on a serving platter and sprinkle with the scallions. Serve immediately.