In a bowl, combine soy sauce, brown sugar, cornstarch, garlic, ginger, and red pepper flakes (if using). Whisk until smooth and set aside.
Heat the vegetable oil in a large skillet over medium-high heat. Add the sliced flank steak and cook until browned, about 3-4 minutes.
Pour the sauce mixture over the beef in the skillet. Stir to coat the beef evenly.
Reduce the heat to low and let simmer for about 10-15 minutes, stirring occasionally, until the sauce thickens.
Stir in the chopped green onions just before serving.
Serve the Mongolian beef over cooked rice.