Rub beef steaks evenly with ginger. Place steaks on rack in broiler pan so surface of beef is 3 to 4 inches from heat. Broil 13 to 17 minutes for medium rare (145°F) to medium (160°F) doneness, turning once.
Meanwhile, combine brown sugar, soy sauce and vinegar in small bowl, stirring until sugar dissolves. Reserve 2 tablespoons mixture for serving. Prepare broccoli according to package directions; drain. Toss with remaining soy mixture. Keep warm.
Carve steaks into slices. Drizzle reserved 2 tablespoons soy mixture over beef. Serve with broccoli.