Slice the beef: Freeze the beef for 15 minutes for easier slicing, then cut thinly against the grain. Place in a bowl.
Marinate: Add 1 tablespoon soy sauce, half the garlic and ginger, and 1 tablespoon cornstarch to the beef.
Toss to coat. Let sit 10–15 minutes while you prep the broccoli and sauce.
Make the sauce: In a small bowl, whisk 1/3 cup soy sauce, 1/3 cup water or broth, rice vinegar, sesame oil, honey, remaining garlic and ginger, and 1 tablespoon cornstarch. Adjust sweetness and heat to taste.
Prep the broccoli: Cut into bite-size florets.
Peel the stalk and slice thinly if you like—don’t waste it. Pat dry to prevent sputtering in the pan.
Heat the pan: Place a large skillet or wok over medium-high heat. Add 1 tablespoon oil and let it shimmer.
Stir-fry the broccoli: Add broccoli and a pinch of salt.
Cook 3–4 minutes, tossing often, until bright green and crisp-tender. Splash in a tablespoon of water if the pan gets too dry. Transfer broccoli to a plate.
Sear the beef: Add another teaspoon of oil if needed.
Spread beef in a single layer. Let it sear undisturbed for 60–90 seconds, then stir-fry 1–2 minutes until mostly browned but still slightly pink.
Add sauce: Return broccoli to the pan. Pour in the sauce and toss.
Cook 1–2 minutes until the sauce bubbles and thickens, coating everything. If too thick, add a splash of water; if too thin, simmer another minute.
Taste and finish: Adjust seasoning with a dash more soy sauce or vinegar. Add chili flakes if you want heat.
Remove from heat.
Serve: Spoon over warm brown rice or cauliflower rice. Garnish with green onions and sesame seeds.