In a medium bowl, whisk together soy sauce, brown sugar, garlic, ginger, 2 teaspoons vegetable oil, and water. Heat soy sauce mixture in a medium saucepan until slightly thickened, about 5-10 minutes; set aside. In a large bowl, combine flank steak and cornstarch. Heat ½ cup vegetable oil in a large saucepan. Add beef and fry until browned and cooked through, about 1-2 minutes. Transfer to a paper towel–lined plate; discard excess oil. Add beef and soy sauce mixture to the saucepan over medium heat and cook until the sauce thickens, about 2-3 minutes. Top with green onions. Serve immediately.