Preparing the Teriyaki Sauce:
In a small saucepan, combine the soy sauce, water, brown sugar, honey, garlic, ginger, and rice vinegar. Bring to a gentle boil over medium-high heat, stirring occasionally.
In a separate bowl, dissolve the cornstarch in the remaining water and add it to the saucepan. Stir constantly as the mixture boils for about one minute until it thickens. Remove from heat and set aside.
Cooking the Chicken:
Brush both sides of the chicken breasts with 1 1/2 tablespoons of olive oil and season with black pepper. There’s no need for salt due to the sodium content of the teriyaki sauce.
Preheat the grill to a medium-high temperature, about 425-450°F (220-230°C). Lightly oil the grill grates, then cook the chicken for approximately 4 minutes per side or until the internal temperature reaches 160-165°F (70-73°C). Let the chicken rest for 5 minutes before dicing it into cubes.
Cooking the Vegetables:
Heat the remaining 2 tablespoons of olive oil in a sauté pan over medium-high heat. Add the zucchini, broccoli, and carrots, and sauté for 4-5 minutes until they are crisp-tender.
Assembling the Bowls:
Arrange the rice in four bowls, then top each with an equal portion of the diced chicken and sautéed vegetables. Drizzle the desired amount of teriyaki sauce over the top, reserving any leftover sauce for later use. Optionally, sprinkle with sesame seeds for added texture. Serve immediately while warm.