In a bowl, combine the soy sauce, sesame oil, brown sugar, garlic, and ginger. Add the sliced flank steak and marinate for at least 30 minutes, or up to 2 hours in the refrigerator for more flavor.

Heat the vegetable oil in a large skillet or wok over medium-high heat. Remove the steak from the marinade, allowing excess marinade to drip off, and add it to the skillet. Cook for 3-4 minutes until browned and cooked through. Remove the beef from the skillet and set aside.

In the same skillet, add the broccoli and carrots. Stir-fry for about 3-5 minutes until the vegetables are tender-crisp.

Return the cooked beef to the skillet with the vegetables, and toss to combine. Season with salt and pepper to taste.

To serve, place a generous scoop of cooked rice in a bowl, top with the beef and vegetable mixture, and garnish with sliced green onions and sesame seeds.