Prep the chicken. Slice chicken into thin strips, about 1/4 inch thick, against the grain. Pat dry.
Toss with a pinch of salt and pepper. Set aside.
Make the sauce. In a small bowl, whisk 1/3 cup tamari or coconut aminos, 1 tablespoon rice vinegar, 1 teaspoon toasted sesame oil, 1–2 teaspoons low-carb sweetener (optional), 1 teaspoon grated ginger, and 2 minced garlic cloves. If using heat, add a pinch of red pepper flakes.
Set aside.
Prep the veggies. Cut broccoli into small florets. Slice bell pepper and zucchini into thin strips. Trim snap peas or cut green beans into bite-size pieces.
Slice mushrooms if using. Keep veggies in separate piles according to how fast they cook.
Heat the pan. Place a large skillet or wok over medium-high to high heat. Add 1 tablespoon oil and swirl to coat.
Sear the chicken. Add half the chicken in a single layer.
Cook 2–3 minutes per side until golden with just-cooked centers. Remove to a plate. Repeat with remaining chicken, adding a little oil if needed.
Do not crowd the pan.
Stir fry the hardy veggies. Add another teaspoon of oil if the pan is dry. Toss in broccoli and green beans or snap peas. Stir fry 2–3 minutes until they brighten and get a bit tender at the edges.
Add the quick-cook veggies. Stir in bell pepper, zucchini, and mushrooms.
Cook 2–3 minutes more, stirring often. Veggies should be crisp-tender, not soft.
Return chicken and add sauce. Add chicken and any juices back to the pan. Pour in the sauce and toss to coat.
Let it bubble for 1–2 minutes to reduce slightly. For a thicker glaze, sprinkle a tiny pinch of xanthan gum over the surface and toss quickly. Use very little—about 1/16 teaspoon—so it doesn’t get gummy.
Finish and taste. Turn off the heat. Drizzle with a small splash of toasted sesame oil.
Taste and adjust salt, acidity, or heat. Top with sliced green onions and sesame seeds.
Serve. Spoon over warm cauliflower rice or a bed of lightly sautéed shredded cabbage for a filling, low-carb base.