Add the ingredients for the teriyaki sauce to a small bowl or measuring cup and stir until combined. Set aside until ready to use. Note: if you’re using store-bought teriyaki sauce, skip this step.
Heat the avocado oil over medium-high heat in a large thick-bottomed pot such as a Dutch oven. A large skillet such as a 12-inch nonstick skillet or sauté pan will work too if it has a deep lip. Add the chopped onion and sauté for 3-4 minutes, or until it begins to soften.
Add the chopped cabbage, grated carrot, and bell pepper and cover the pot or skillet. Cook, stirring occasionally, until the cabbage has wilted, about 8 to 10 minutes.
Scoot the vegetables off to one side of the pot (or skillet) and add the chopped chicken and green onions. Allow the chicken to brown for 5 to 8 minutes, giving it a stir or two while keeping it separate from the vegetables. After the chicken has browned, stir it in with the vegetables.
Cover the pot and continue cooking over medium high heat, stirring occasionally, until the chicken has cooked through, about 8 to 15 minutes. Chicken is fully cooked with it reaches an internal temperature of 165 degrees F. The exact cooking time depends on your desired level of doneness and also the temperature of all of the ingredients going into the pot.
Pour the teriyaki sauce into the pot and stir well until everything is coated with sauce. Continue cooking at a high heat and stirring until much of the liquid has burned off (if it hasn’t already).
Taste the meal for flavor and add more liquid aminos (or soy sauce), vinegar, fresh lime juice, kosher salt, black pepper, etc. to your personal taste. Sprinkle with sesame seeds and extra chopped green onions if you'd like.
You can serve this meal with additional side dishes like brown rice, cauliflower rice or extra sauteed vegetables.
Serve Teriyaki Chicken and Cabbage in large bowls, and enjoy! Serve with lime wedges and extra teriyaki sauce for drizzling over the meal.