Heat the vegetable oil in a large skillet or wok over medium-high heat. Add the sliced flank steak and cook until browned, about 3-4 minutes. Remove the beef from the skillet and set aside.
In the same skillet, add the sliced bell peppers, onion, garlic, and ginger. Stir-fry for about 3-4 minutes until the vegetables are tender-crisp.
In a small bowl, whisk together the soy sauce, brown sugar, rice vinegar, chili paste, and sesame oil. Pour this sauce over the vegetables in the skillet and bring to a simmer.
Return the cooked beef to the skillet and toss everything together until the beef is coated in the sauce and heated through, about 2-3 minutes.
Serve immediately, garnished with chopped green onions and sesame seeds.