Combine soy sauce, 1 tablespoon cornstarch, and sesame oil in a bowl. Add sliced flank steak, tossing to coat. Marinate for 15-30 minutes.
Blanch broccoli florets in boiling water for 2 minutes, then transfer to an ice bath. Drain and set aside.
Heat 1 tablespoon olive oil in a large pan over high heat until shimmering. Add beef in a single layer, searing until browned, about 2-3 minutes per side.
Remove beef from the pan and set aside. Add remaining olive oil, ginger, and garlic, sautéing until fragrant, about 30 seconds.
Stir in broccoli, cooking until heated through, about 2 minutes. Return beef to the pan.
Mix beef broth, remaining cornstarch, and sugar in a small bowl. Pour into the pan, stirring to combine and thicken the sauce.
Cook until the sauce coats the beef and broccoli, about 2 minutes. Season with salt and pepper to taste.
Serve immediately, garnished with sesame seeds if desired.