In a small saucepan over medium-high heat, combine the soy sauce, mirin, brown sugar, and ginger. Stir continuously for a few minutes until the mixture bubbles and thickens. Remove from the heat and let cool slightly.
Meanwhile, steam the purple broccoli for about 5 minutes, until tender but still with a little bite. Alternatively, blanch in boiling water for 2–3 minutes.
Arrange the broccoli on a serving platter.
Mix the cooled teriyaki sauce with the mayonnaise until smooth, then drizzle generously over the broccoli.
Sprinkle with sesame seeds before serving, if desired.