In a blender or food processor, combine the olive oil, miso, vinegar, salt, sesame oil, honey, ginger, garlic, and water. Blend until smooth. Stir in the minced shallot.
In a large bowl, combine the Romaine, cabbage, chicken, oranges, cilantro, almonds, and sesame seeds. Drizzle with the dressing and toss to combine. Serve immediately.