In a bowl, toss the sliced flank steak with cornstarch until well 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 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 and set aside.
In the same skillet, add the chopped green onions and minced garlic. Stir-fry for about 30 seconds until fragrant.
In a small bowl, whisk together the soy sauce, brown sugar, ginger, and red pepper flakes (if using). Pour this mixture into the skillet and bring to a simmer.
Return the cooked beef to the skillet and toss to coat in the sauce. Cook for an additional 2-3 minutes until the sauce thickens slightly.
Serve the Mongolian beef over cooked rice and garnish with additional green onions if desired.