In a medium bowl, combine the thinly sliced flank steak with soy sauce and cornstarch. Mix well and let it marinate for about 5 minutes.

Heat vegetable oil in a large skillet over medium-high heat and add the marinated beef in a single layer. Cook for 2-3 minutes on each side until browned.

Remove the beef from the skillet and set aside. In the same skillet, add more oil if needed, and sauté minced garlic and grated ginger for about 30 seconds.

Add brown sugar and water to the pan, stirring until the sugar dissolves. Allow to simmer and thicken for 1-2 minutes.

Return the cooked beef to the skillet, toss in the sauce, and cook for another 1-2 minutes until heated through.

Transfer the Mongolian Beef to a serving dish, garnish with sliced green onions, and serve hot over a bed of cooked rice.