Slice the beef. Pat the steak dry and slice very thinly against the grain.
Aim for 1/8-inch slices. Partially freezing the steak for 20–30 minutes makes this easier.
Tenderize and marinate. In a bowl, toss the beef with 2 tablespoons tamari (from your 1/3 cup), 1/2 teaspoon baking soda, and a pinch of pepper. Let sit for 10–15 minutes while you prep everything else.
Make the sauce. In a small bowl, whisk together remaining tamari, beef broth, sesame oil, vinegar, sweetener, garlic, ginger, and a pinch of red pepper flakes if using.
Taste and adjust salt, sweetener, or acidity. If you want a thicker sauce, sprinkle in xanthan gum and whisk well; a little goes a long way.
Prep the broccoli. Cut into bite-size florets. Rinse and shake dry.
If the stems are thick, peel and slice them thin so they cook evenly.
Stir-fry the broccoli. Heat a large skillet or wok over medium-high. Add 1 tablespoon oil. When shimmering, add broccoli and a pinch of salt.
Stir-fry 3–4 minutes until crisp-tender with bright color. Transfer to a plate.
Cook the beef. Add another 1 tablespoon oil to the hot pan. Spread the beef in a single layer.
Let it sear undisturbed for 60–90 seconds, then stir-fry until just browned, 2–3 minutes total. Don’t overcook.
Combine and sauce. Return broccoli to the pan. Pour in the sauce.
Toss to coat and simmer 1–2 minutes until glossy and slightly thickened. If it gets too thick, splash in a bit more broth.
Finish and serve. Taste and adjust seasoning. Garnish with sliced green onions and sesame seeds.
Serve hot as is, or over cauliflower rice or zucchini noodles.