In a mixing bowl, toss the sliced flank steak with cornstarch until well coated. Allow it to sit for about 5 minutes while you prepare the sauce.
In a separate bowl, whisk together soy sauce and brown sugar until the sugar dissolves. Set aside.
Heat 2 tablespoons of vegetable oil in a large skillet or wok over medium-high heat. Once hot, add the coated beef slices in a single layer and cook for about 2-3 minutes until browned, flipping once. Remove the beef from the pan and set aside.
In the same skillet, add the remaining tablespoon of oil. Add minced garlic and ginger, sautéing for about 30 seconds until fragrant.
Pour in the soy sauce and brown sugar mixture, stirring until it begins to thicken slightly, around 1-2 minutes.
Return the cooked beef to the skillet, tossing to coat it in the sauce. Sprinkle in red pepper flakes if desired and cook for an additional 2 minutes.
Stir in the chopped green onions just before serving, reserving a few for garnish.
Serve the Mongolian Beef hot over cooked rice, garnished with additional green onions if desired.