Marinate the Meat: In a mixing bowl, whisk together soy sauce, balsamic vinegar, olive oil, brown sugar, minced garlic, black pepper, red pepper flakes, Worcestershire sauce, and dried rosemary. Place the London Broil in a large resealable bag and pour in the marinade. Seal and refrigerate for at least 4 hours, preferably overnight.
Preheat the Broiler: Set your oven's broiler on high and position the rack about 4 inches from the heat source.
Prepare for Broiling: Remove the meat from the marinade and place it on the broiling pan. Discard the remaining marinade.
Broil the Meat: Broil the London Broil for 7-8 minutes on each side for medium-rare, or longer depending on your desired doneness. Use a meat thermometer to check that the internal temperature reaches 135°F for medium-rare.
Rest the Meat: Remove the meat from the oven and loosely cover it with aluminum foil. Let it rest for 10 minutes to allow the juices to redistribute.
Slice and Serve: Slice the meat thinly against the grain and serve immediately.