In a saucepan over medium heat, combine ¾ cup water, brown sugar, soy sauce, honey, sesame oil, ginger, and garlic powder. Stir and bring to a gentle simmer.
In a small bowl, whisk together the cornstarch and remaining ¼ cup cold water until smooth.
Slowly whisk the cornstarch mixture into the sauce, stirring constantly. Let it simmer for 2–3 minutes, until thickened, then remove from heat and set aside.
Heat a large skillet over medium-high heat and add the oil. Season the cubed chicken with salt and pepper.
Cook the chicken for 3–4 minutes per side, until fully cooked and lightly browned.
Pour the teriyaki sauce over the chicken and toss to coat, cooking for another 1–2 minutes until everything is heated through.
Assemble the bowls with a base of rice, then top with the teriyaki chicken, broccoli, carrots, and cucumber.
Finish with green onions and sesame seeds before serving.