In a large bowl, combine the sliced flank steak with soy sauce, cornstarch, brown sugar, black pepper, and red pepper flakes (if using). Mix well and let marinate for at least 15 minutes.
Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat. Add the marinated steak in a single layer and cook for about 2-3 minutes until browned. Remove the steak from the skillet and set aside.
In the same skillet, add the remaining tablespoon of oil. Add the sliced onion, red bell pepper, and green bell pepper. Stir-fry for about 3-4 minutes until the vegetables are tender-crisp.
Add the minced garlic and ginger to the skillet and stir-fry for an additional 1 minute until fragrant.
Return the cooked steak to the skillet and toss everything together. Cook for another 2-3 minutes until heated through and the sauce thickens slightly.
Serve hot over cooked rice or noodles and garnish with chopped green onions.