Toss kale, cabbage, cranberries, carrots, sunflower seeds, and shallot together in a large bowl.
Mix rice vinegar, mirin, soy sauce, sugar, ginger, garlic, avocado oil, and sesame oil together in a separate bowl; pour over kale mixture and toss to coat salad thoroughly.
Chill salad in refrigerator until softened and flavors meld, 2 hours to overnight.