Place the chicken in a bowl with 1 tablespoon of the soy sauce, salt, and pepper. Stir to coat. Sprinkle 1 teaspoon of the cornstarch over the top and stir once more. Set aside.
In a medium bowl or large liquid measuring cup with a spout, whisk together the water, honey, rice vinegar, garlic, ginger, red pepper flakes, and the remaining 1/4 cup soy sauce and 2 teaspoons cornstarch until smoothly combined. Set near the stove.
In a large nonstick skillet or wok, heat the oil over medium-high heat. Once the oil is hot and shimmering, add the chicken in a single layer. Let cook undisturbed on the first side until deeply golden, about 2 to 3 minutes, then turn the chicken pieces and continue cooking until the chicken is browned all over and cooked through, about 2 to 3 minutes more.
Towards the end of the cooking time, steam the vegetables (if using).
Pour in the sauce and stir to coat the chicken. Let simmer, stirring frequently, until the sauce thickens and looks sticky and glossy, about 1 to 2 minute. Stir in about two-thirds of the green onions. Serve hot with rice, steamed vegetables, and a sprinkle of the remaining green onions.
TO STORE: Refrigerate teriyaki chicken in an airtight storage container for up to 4 days.
TO REHEAT: Rewarm leftovers in a skillet on the stovetop over medium-low heat or in the microwave.
TO FREEZE: Freeze teriyaki chicken in an airtight freezer-safe storage container for up to 3 months. Let thaw overnight in the refrigerator before reheating.