Prep: Cut chicken into 1″ pieces, trim broccoli into even florets. Pat chicken dry and season lightly with pepper. Whisk tamari, rice vinegar, powdered sweetener, ginger, garlic, and 30 ml broth in a bowl; set aside.
Heat pan: Add avocado oil to a large skillet/wok over high heat until shimmering. Add chicken in a single layer; sear 2–3 minutes per side until browned and nearly cooked. Remove to a plate.
Sear broccoli: Add broccoli to the hot pan with a splash (1–2 tbsp) broth. Toss 2 minutes until bright green; optionally cover for 1 minute for slightly softer stems.
Combine & simmer: Return chicken to pan. Pour the sauce over chicken and broccoli, stirring to combine. Bring to a gentle simmer for 1–2 minutes.
Thicken: Sprinkle xanthan gum evenly while whisking briskly; sauce will thicken within a minute. Adjust thickness with extra broth if needed.
Finish: Remove from heat, stir in toasted sesame oil and lime juice. Season with salt if needed. Garnish with toasted sesame seeds and green onions. Serve hot.