Combine the water, soy sauce, ginger, garlic, and honey in a small saucepot over medium heat. Meanwhile, in a small bowl, whisk together the arrowroot powder and water. Once the soy sauce mixture is simmering slightly, add the arrowroot slurry and stir constantly until combined and sauce is thickened. Set aside.
Heat the oil in a wok or large skillet and add in the broccoli and cook for 3-5 minutes or until crisp tender and add in the bell peppers, zucchini noodles, and toss well to combine. Let cook for 3 minutes until vegetables are crisp tender.
Meanwhile, scramble the eggs.
Add the scrambled egg to the wok or skillet and pour over the teriyaki sauce and toss well to combine and coat everything in the teriyaki sauce.
Serve, garnished with sesame seeds, if using.