Whisk the sauce: in a small bowl or measuring cup, combine 1 Tbsp avocado oil, 5 Tbsp liquid aminos or soy sauce, 2 Tbsp rice vinegar, 2 Tbsp maple syrup or honey, minced garlic, grated ginger, and tapioca flour or cornstarch until smooth; set aside.
Heat 1 Tbsp avocado oil in a large pot or 12-inch skillet over medium-high heat until shimmering.
Add the chopped onion and sauté 3–4 minutes until it begins to soften.
Add the sliced cabbage, grated carrot, and red bell pepper; cover and cook, stirring occasionally, until the cabbage wilts, about 8–10 minutes.
Push the vegetables to one side of the pan and add the chopped chicken and most of the chopped green onions; cook the chicken undisturbed for 5–8 minutes to brown, stirring once or twice while keeping it separate from the vegetables.
Stir the browned chicken into the vegetables, cover, and continue cooking over medium-high heat until the chicken reaches 165°F and is cooked through, about 8–15 more minutes.
Pour the prepared teriyaki sauce into the pot and stir to coat everything; cook at high heat, stirring, until the sauce thickens and excess liquid reduces.
Taste and adjust seasoning with more liquid aminos/soy sauce or a pinch of sea salt if needed, then sprinkle with remaining green onions and sesame seeds if desired.
Serve the teriyaki chicken and cabbage in bowls with lime wedges and extra sauce as desired.
