Combine the sliced flank steak, soy sauce, and cornstarch in a bowl. Mix well to coat the beef evenly and let it marinate for 15 minutes.

In a small bowl, whisk together soy sauce, water, brown sugar, and cornstarch slurry until smooth. Set aside.

Heat oil in a large pan or wok over medium-high heat. Add the marinated beef in a single layer and cook for about 2-3 minutes on each side until the beef is browned and cooked through. Remove the beef from the pan and set aside.

In the same pan, add another 2 tablespoons of vegetable oil. Add minced garlic, chili flakes and ginger, and sauté for about 1 minute until fragrant.

Pour the sauce mixture into the pan, stirring constantly until it thickens and becomes glossy, about 2-3 minutes.

Add the cooked beef back into the pan along with the green onions (and red bell pepper and carrots if using). Stir-fry for another 2-3 minutes until everything is well coated with the sauce and heated through.

Serve the Mongolian beef hot over steamed rice or noodles.