Prep the beef: Place the steak in the freezer for 20–30 minutes to firm up. Slice very thin against the grain.
Pat dry with paper towels for better browning.
Make the sauce: In a small bowl, whisk tamari, beef broth, rice vinegar, sesame oil, sweetener, and chili flakes. If using xanthan gum, sprinkle it over the surface and whisk vigorously to avoid clumps. Set aside.
Blanch or steam the broccoli: Bring a pot of water to a boil and blanch florets for 1–2 minutes until bright green and crisp-tender.
Drain well and set aside. Or steam briefly in the microwave with a splash of water.
Heat the pan: Set a large skillet or wok over medium-high heat. Add 1 tablespoon oil and swirl to coat.
Sear the beef in batches: Add half the beef in a single layer.
Season lightly with salt and pepper. Sear 60–90 seconds per side until just browned. Remove to a plate and repeat with remaining oil and beef.
Don’t overcrowd the pan.
Stir-fry aromatics: Lower heat to medium. Add garlic, ginger, and the white parts of green onions. Stir about 30 seconds until fragrant, scraping up browned bits.
Add broccoli and sauce: Return heat to medium-high.
Add broccoli and pour in the sauce. Toss and cook 1–2 minutes, letting the sauce bubble. If not using xanthan gum, simmer a bit longer to reduce and thicken.
Finish with beef: Return the beef and any juices to the pan.
Toss until coated and warmed through, about 1 minute. Taste and adjust seasoning—more tamari for salt, vinegar for brightness, or sweetener for balance.
Garnish and serve: Remove from heat. Sprinkle with sesame seeds and the green parts of the onions.
Serve over cauliflower rice and add a squeeze of lime if you like.