Pat the chicken breast dry and season with sea salt and black pepper.
Heat avocado oil in a large skillet or wok over medium-high heat.
Add the chicken to the skillet and cook until golden brown and cooked through, about 5 to 7 minutes.
Remove chicken from the pan and set aside.
In the same pan, add the shredded cabbage, minced garlic, and grated ginger, sautéing until the cabbage is slightly softened but still crisp.
Whisk together the tamari, toasted sesame oil, and rice vinegar in a small bowl.
Return the chicken to the pan and pour the sauce over the mixture, tossing well to coat.
Garnish with sliced green onions and serve immediately.