Drain, rinse and set aside noodles (prepare according to package directions.)
Return pan to heat and add remaining olive oil. Add the garlic, ginger, and broccoli. Cook until the vegetables are just crisp tender, about 2-3 minutes.
Meanwhile, whisk together the coconut aminos, fish sauce, sweetener, remaining 1/2 teaspoon sesame oil, xanthan gum (if using) and water. Stir into the pan along with the cooked chicken and prepared noodles. Allow sauce to bubble and thicken up and toss to coat well. Adjust seasonings with salt and pepper as needed plus chili flakes or Sriracha if desired.
Serve hot and garnish with sesame seeds, green onions, and carrots, if desired.