Heat a large skillet or wok over medium-high heat and add the cooking oil.
Add the ground beef and cook until browned, breaking it apart with a spoon.
Add the chopped onion and cook for 2 minutes until softened.
Stir in the garlic and ginger and cook for 30 seconds until fragrant.
Add bell peppers, broccoli, and carrots. Stir-fry for 4–5 minutes until tender-crisp.
In a small bowl, mix soy sauce, oyster sauce, hoisin sauce, cornstarch, and water.
Pour the sauce into the pan and stir well. Cook for 2–3 minutes until thickened.
Taste and adjust seasoning. Add red pepper flakes if desired.
Remove from heat and serve immediately.