In a bowl, toss the sliced flank steak with cornstarch until evenly coated. Let it sit for about 10 minutes to allow the cornstarch to adhere.
In a large skillet or wok, heat the vegetable oil over medium-high heat. Add the coated beef in a single layer and cook for 2-3 minutes until browned. You may need to do this in batches to avoid overcrowding the pan.
Remove the beef from the skillet and set aside. In the same skillet, add soy sauce, brown sugar, garlic, ginger, and red pepper flakes. Stir well and bring to a simmer.
Return the beef to the skillet and toss to coat in the sauce. Cook for an additional 2-3 minutes until the sauce thickens slightly.
Stir in the chopped green onions and cook for another minute. Remove from heat.
Serve the Mongolian beef over cooked rice.