Place sliced steak in a gallon-sized resealable bag.
In a small bowl, whisk together soy sauce, brown sugar, garlic, sesame oil, ground ginger and red pepper paste. Pour over steak, seal bag and marinate in the refrigerator for at least 4 hours (preferably overnight).
Heat oil in a large skillet over medium-high heat. Working in batches, add steak to the pan and cook for 2-3 minutes on each side.
Meanwhile, add marinade to a saucepan over medium-high heat. In a small bowl, whisk together cornstarch and water to make a slurry then whisk into the saucepan. Bring to a boil and let cook until thickened.
Toss cooked steak in sauce then garnish with green onion and sesame seeds before serving.