Marinate beef slices in half of the soy sauce for 10 minutes.
Heat 1 tablespoon vegetable oil in a large skillet or wok over medium-high heat.
Cook broccoli florets in oil until tender-crisp, about 3-4 minutes. Remove and set aside.
Add remaining oil to the same pan and cook marinated beef until done, about 3-5 minutes.
Add minced garlic and grated ginger to the beef, cooking for 30 seconds until fragrant.
Mix remaining soy sauce, cornstarch, sesame oil, and sugar in a small bowl to create sauce.
Return broccoli to the pan with beef and add sauce mixture.
Stir-fry everything together until sauce thickens and coats ingredients, about 2-3 minutes.