In a large bowl, whisk together the rice vinegar, toasted sesame oil, coconut aminos, grated fresh ginger, sea salt, and black pepper to create the dressing base.
Add the shredded green cabbage, red cabbage, shredded carrots, and shelled edamame to the bowl and toss thoroughly until the vegetables are evenly coated.
Heat the avocado oil in a non-stick skillet over medium-high heat until shimmering.
Place the chicken gyoza in the skillet and sear for 2 to 3 minutes until the bottoms are golden and crispy.
Carefully add a splash of water to the pan and immediately cover with a lid to steam the gyoza for 2 minutes, then remove the lid and cook until any remaining moisture evaporates.
Slice the pre-cooked chicken breast into thin, bite-sized strips.
Transfer the dressed cabbage salad to a serving plate and top with the hot, crispy gyoza and the sliced chicken breast.
Garnish the dish with thinly sliced green onions and serve immediately while the gyoza are still warm.