In a medium bowl, combine the sliced flank steak, soy sauce, sesame oil, and cornstarch. Mix well to ensure all beef pieces are coated with the marinade. Let it sit for about 10-15 minutes while you prepare the vegetables.

Wash and cut the broccoli florets and bell pepper. Mince the garlic and grate the ginger. Having all your ingredients prepped and ready will streamline the cooking process.

In a large skillet or wok, heat 1 tablespoon of vegetable oil over medium-high heat. Once the oil is hot, add the marinated beef in a single layer. Cook the beef for about 3-4 minutes, turning occasionally, until it is browned and just cooked through. Remove the beef from the skillet and set it aside.

In the same skillet, add the remaining tablespoon of vegetable oil. Add the broccoli and bell pepper, stir-frying for about 3-4 minutes until they are vibrant and tender-crisp.

Once the vegetables are cooked to your liking, add the minced garlic and grated ginger. Stir for about 30 seconds until fragrant. Be careful not to burn the garlic.

Return the cooked beef to the skillet. Pour in the teriyaki sauce, and stir well to combine all the ingredients. Allow the mixture to cook for an additional 2-3 minutes.

Turn off the heat and transfer the teriyaki beef and broccoli to a serving platter. Garnish with chopped green onions and a sprinkle of sesame seeds if desired. Serve hot over steamed rice or noodles.