Place the chicken pieces in a zip-top bag or container with 1/2 cup coconut aminos, 1/3 cup rice vinegar, and 4 minced garlic cloves (or 2 tsp garlic powder). Seal, toss to coat, and refrigerate at least 20 minutes or up to overnight.
Heat 3 Tbsp avocado oil in a large deep skillet over medium-high heat. Add the sliced half onion and sauté, stirring occasionally, until softened and translucent, about 6–8 minutes.
Add the shredded cabbage to the skillet (it may heap up). Stir as best you can, then cover and cook until the cabbage wilts and begins to reduce, about 3–5 minutes.
Remove the cover and stir in 3 minced garlic cloves, 1 Tbsp grated fresh ginger, 1/2 tsp ground cumin, and 3 Tbsp coconut aminos. Cook, stirring occasionally, until the edges of the cabbage begin to brown, about 5–8 minutes.
Push the cabbage mixture to one side of the skillet. Add the marinated chicken (including any marinade) to the empty side and let it brown undisturbed for 3–4 minutes.
Stir the chicken into the cabbage, then add the chopped carrots and zucchini. Continue cooking, stirring frequently, until the chicken is cooked through and the vegetables are tender and excess liquid has mostly evaporated, about 5–8 minutes more.
Stir in the chopped green onions, taste and adjust seasoning if desired, then serve immediately topped with sesame seeds.