Prep the beef: Pat the steak dry and slice it thinly against the grain.
Season lightly with salt and black pepper. Set aside while you make the sauce.
Mix the sauce: In a small bowl, whisk together beef broth, tamari or coconut aminos, vinegar, sesame oil, sweetener, and tomato paste. Sprinkle in xanthan gum and whisk until smooth.
Taste and adjust sweetness or salt.
Cook the broccoli: Heat 1 tablespoon oil in a large skillet over medium-high heat. Add broccoli and a pinch of salt. Stir-fry 3–4 minutes (5–6 if frozen) until crisp-tender.
Transfer to a plate.
Sear the beef: Add remaining oil to the skillet. Increase heat to high. Add beef in a single layer (work in batches to avoid steaming).
Sear 1–2 minutes per side until browned with pink inside. Transfer to the plate with broccoli.
Sauté aromatics: Reduce heat to medium. Add garlic, ginger, and the white parts of the green onions.
Cook 30–45 seconds until fragrant. Add red pepper flakes if using.
Combine and sauce: Return beef and broccoli to the pan. Pour in the sauce and toss.
Simmer 1–2 minutes until it thickens and coats everything. If it gets too thick, splash in a bit more broth.
Finish and serve: Top with green onion tops and sesame seeds. Taste and adjust seasoning.
Serve as is, or over cauliflower rice for a bigger meal.