Whisk together water, soy, honey, vinegar, garlic, ginger, and pepper.
Heat a large frying pan over medium-high heat. Add oil to the pan. When hot, add the chicken pieces in a single layer. Brown on one side about 5 minutes then turn and cook until almost cooked through (5-8 more minutes, depending on the size of the pieces)
Add the teriyaki sauce to the pan and cook until chicken is cooked through.
Meanwhile, mix cornstarch with 1-2 teaspoons of cold water to make a slurry. Add it to the pan and stir to combine. Cook a few more minutes, the sauce will boil and thicken. Once thickened, remove from heat.
Serve hot over rice with a garnish of green onions.
Teriyaki sauce can also be used as a marinade. Add chicken or beef to the sauce and let sit at least 2 hours before cooking. Discard marinade after soaking, do not use it as a sauce.