In a bowl, whisk together soy sauce and cornstarch. Add beef and toss to coat. Let it marinate for 10 minutes.
Heat sesame oil in a large skillet or wok over medium-high heat. Add beef and cook until browned, about 3-4 minutes. Remove beef and set aside.
Add garlic and ginger to the skillet and cook for 30 seconds until fragrant. Add broccoli florets and cook for 3-5 minutes, or until tender-crisp.
In a small bowl, whisk together brown sugar, water, and red pepper flakes (if using). Pour sauce into the skillet and bring to a simmer. Cook until sauce thickens slightly, about 1-2 minutes.
Return beef to the skillet and toss to coat with sauce. Cook for 1 minute more, or until heated through.
Serve immediately over rice or noodles.
Notes
Garnish with sesame seeds and chopped green onions, if desired.