Heat the vegetable oil in a large skillet or wok over medium-high heat. Add the minced garlic and ginger, sautéing for about 30 seconds until fragrant.
Add the ground beef to the skillet, breaking it apart with a spatula. Cook until browned and fully cooked, about 5-7 minutes. Drain excess fat if necessary.
Stir in the broccoli florets and cook for another 3-4 minutes until they are bright green and tender-crisp.
In a small bowl, mix the soy sauce, teriyaki sauce, cornstarch, water, and red pepper flakes (if using). Pour this sauce over the beef and broccoli mixture, stirring to coat everything evenly.
Cook for an additional 2-3 minutes, allowing the sauce to thicken slightly. Drizzle with sesame oil before serving.
Serve hot over cooked rice or quinoa.