Condition the Sirloin : In a small bowl, toss the thinly sliced sirloin with 1 tablespoon of the tamari and the full ¾ teaspoon of toasted sesame oil. Let it stand at room temperature while you prepare the other components.
Flash-Sear the Steak : Place your cast-iron skillet over medium-high heat and add 1 tablespoon of avocado oil. Once the oil shimmers, carefully place the steak slices in a single, uncrowded layer. Cook for 60-90 seconds per side, just until a rich brown crust forms. Use tongs to transfer the seared steak to a clean plate. Do not wipe the skillet clean.
Bloom the Aromatics : Lower the heat to medium and add the remaining ½ tablespoon of avocado oil. Add the minced garlic and grated ginger to the skillet, stirring constantly for about 45 seconds until their aroma is potent.
Steam-Fry the Broccoli : Toss the broccoli florets into the skillet with the aromatics. Pour in the ¼ cup of beef broth and immediately cover the pan. Allow the broccoli to steam for 3–4 minutes. The goal is a vibrant green color and a texture that is firm yet easily pierced with a fork.
Forge the Pan Sauce : Remove the lid. Add the remaining 2 tablespoons of tamari, the rice vinegar, and the chili garlic sauce to the skillet, stirring to coat the broccoli. Evenly dust the xanthan gum over the contents and stir briskly for about 30 seconds. The sauce will bubble and visibly tighten.
Reunite & Finish : Return the seared sirloin and any juices from the plate back into the skillet. Fold all the ingredients together for 1–2 minutes, allowing the sauce to glaze every piece and ensuring the beef is warmed through. The final dish is ready when the sauce clings beautifully to the steak and broccoli.
Garnish & Plate : Remove the skillet from the heat. Serve immediately, dividing the mixture among three plates. Top with a flourish of toasted sesame seeds and fresh, thinly sliced scallions. This dish is excellent on its own or served alongside cauliflower rice to maintain its low-carb integrity.