Blanch the broccoli and plunge into ice cold water to stop the cooking. Drain and set aside.
Prepare the teriyaki by diluting the arrowroot in 2 tbsp of cold water.
Heat the remaining water, soy sauce, garlic, and ginger. Add the honey and stir to dissolve. Add the arrowroot mixture and the pepper. Continue stirring to thicken. There should be about 2/3 cup sauce.
Toss the broccoli with 1/3 cup of sauce and serve.