Combine the rice vinegar, sesame oil, miso paste, and mayonnaise in a small bowl or jar; shake or whisk to blend thoroughly. Add the ginger and garlic powder.
In a serving bowl, toss the broccoli florets with the finely chopped red onion; add shredded carrot, if using.
Pour the dressing over the broccoli and toss to blend ingredients.
Cover the bowl and chill thoroughly before serving.