In a medium bowl, combine the sliced beef, soy sauce, oyster sauce, and cornstarch. Mix well and let marinate for 10 minutes.
Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat.
Add the marinated beef to the skillet in a single layer and cook for 3-4 minutes, stirring occasionally, until browned and just cooked through. Remove the beef from the skillet and set aside.
Add the remaining 1 tablespoon of vegetable oil to the skillet.
Add the minced garlic and grated ginger, sauté for 30 seconds until fragrant.
Add the red bell pepper, green bell pepper, carrot, and broccoli florets to the skillet. Stir-fry for 5-6 minutes until the vegetables are tender-crisp.
Return the cooked beef to the skillet with the vegetables.
Pour in the beef broth and sesame oil, stirring to combine all ingredients.
Season with black pepper and crushed red pepper flakes. Stir-fry for another 2 minutes to heat through and allow flavors to meld.
Remove from heat and garnish with sliced green onions before serving.