Prep the steak: Pat the flank steak dry with paper towels. Slice it thinly against the grain, about 1/4 inch thick.
Season lightly with salt and pepper.
Make the sauce base: In a small bowl, whisk together tamari or coconut aminos, brown erythritol, rice vinegar, and beef broth. Set aside.
Heat the pan: Use a large skillet or wok over medium-high heat. Add 1–2 tablespoons of avocado oil and let it shimmer.
Sear in batches: Add a single layer of steak to the hot pan.
Cook 1–2 minutes per side until the edges get crispy and browned but the centers stay tender. Remove to a plate and repeat with remaining steak, adding more oil if needed.
Sauté aromatics: Drop heat to medium. Add butter (if using), then the minced garlic and grated ginger.
Cook 30–45 seconds until fragrant, stirring constantly so they don’t burn.
Add the sauce: Pour in the sauce mixture. Bring to a gentle simmer, stirring to dissolve the sweetener. Taste and adjust sweetness or salt as needed.
Thicken smartly: Sprinkle in xanthan gum while whisking to avoid clumps.
Start with 1/8 teaspoon, then add a pinch more if needed. Simmer 1–2 minutes until the sauce turns glossy and lightly coats a spoon.
Combine: Return the seared steak (and any juices) to the pan. Toss to coat every slice.
Add red pepper flakes if you want heat. Simmer 1 minute to marry flavors.
Finish: Stir in half the green onions and the sesame oil. Kill the heat and let everything sit for 1–2 minutes to relax and thicken slightly more.
Serve: Plate with steamed broccoli, cauliflower rice, or sautéed cabbage.
Garnish with remaining green onions and sesame seeds. Enjoy immediately.