Prep everything first. Slice the chicken thin so it cooks fast. Chop veggies into bite-size pieces. Stir together the sauce ingredients in a small bowl.
If using xanthan gum, sprinkle it in while whisking to avoid clumps.
Heat the pan. Set a large skillet or wok over medium-high heat. Add 1 tablespoon oil and swirl to coat. The pan should be hot before the chicken touches it.
Sear the chicken. Add chicken in a single layer.
Season with a pinch of salt and pepper. Cook 4–6 minutes, stirring only a couple of times, until golden and just cooked through. Transfer to a plate.
Cook the veggies in stages. Add the remaining 1 tablespoon oil.
Toss in broccoli and mushrooms first. Stir-fry 2 minutes. Add bell pepper and zucchini.
Cook another 2–3 minutes until crisp-tender.
Add aromatics. Push veggies to the sides. Add garlic, ginger, and the white parts of the green onion to the center. Cook 30 seconds until fragrant.
Stir everything together.
Bring it together. Return the chicken and any juices to the pan. Sprinkle in red pepper flakes if using.
Sauce and thicken. Pour the sauce around the pan. Toss to coat.
If using xanthan gum, the sauce will thicken in about 30–60 seconds. If it gets too thick, add a splash of water.
Finish and serve. Turn off heat. Stir in the green onion tops.
Taste and adjust salt, pepper, or sweetener. Serve over warm cauliflower rice and garnish with sesame seeds and lime if you like.