Heat 1 tbsp sesame oil in a small saucepan over medium heat. Add the garlic and scallions and gently saute for a minute. Reduce the heat and whisk in the honey, miso, and vinegar. Turn the heat back up to medium and cook for 1-2 minutes. Remove from the heat and pour into a mixing bowl.
Whisk in the remaining sesame oil and water. Taste and season with sea salt and black pepper. Place the cabbage, radicchio, snap peas, radish, cilantro, peanuts, scallions, and sesame seeds into a large mixing bowl. Add shredded chicken breast. Toss with some of the vinaigrette to coat. Taste. Add more vinaigrette or salt as needed.