In a bowl, mix soy sauce, brown sugar, and half the garlic and ginger. Add beef and marinate for 30 minutes.
In another bowl, mix cornstarch and water to create a slurry.
Heat oil in a large wok or skillet over high heat.
Add remaining garlic and ginger, stir-fry for 30 seconds.
Add beef (discarding marinade) and stir-fry for 2-3 minutes until browned.
Add broccoli and stir-fry for 3-4 minutes until crisp-tender.
Pour in the cornstarch slurry and cook until sauce thickens.
Garnish with sesame seeds if desired and serve.