In a bowl, toss the sliced flank steak with cornstarch until evenly coated. Let it sit for about 10 minutes.
In a large skillet or wok, heat the vegetable oil over medium-high heat. Add the coated beef in a single layer and cook until browned, about 2-3 minutes per side. Remove the beef from the skillet and set aside.
In the same skillet, add the minced garlic and ginger, and sauté for about 30 seconds until fragrant.
In a small bowl, whisk together the soy sauce, brown sugar, and water. Pour this mixture into the skillet and bring to a simmer.
Return the cooked beef to the skillet and stir to coat in the sauce. Cook for an additional 2-3 minutes until the sauce thickens slightly.
Stir in the chopped green onions and red pepper flakes, if using. Cook for another minute.
Serve the Mongolian beef over cooked rice.