Cook the rice. Prepare 3 cups cooked rice according to package directions.
Fluff and set aside to cool slightly. For extra flavor, add a pinch of salt and a splash of rice vinegar to the water.
Mix the sauce. In a small bowl, whisk soy sauce, honey, rice vinegar, sesame oil, garlic, ginger, and water. Taste and adjust sweetness or saltiness.
In another tiny bowl, mix cornstarch with cold water and set aside.
Prep the chicken. Pat the chicken dry and cut into bite-size pieces. Season lightly with salt and pepper. Pour 3 tablespoons of the teriyaki sauce over the chicken and toss to coat.
Let sit while you prep the veggies.
Chop the veggies. Cut broccoli into small florets. Slice bell peppers into strips, carrots into thin coins, and red onion into wedges. Trim snap peas.
Keep cuts uniform so everything cooks evenly.
Cook the chicken. Heat a large skillet over medium-high with 1/2 tablespoon oil. Add half the chicken in a single layer. Sear 3–4 minutes, flip, and cook another 2–3 minutes until cooked through.
Remove to a plate. Repeat with remaining chicken, adding a touch more oil if needed.
Stir-fry the veggies. In the same pan, add remaining oil. Toss in carrots and onion first; cook 2 minutes.
Add broccoli; cook 3 minutes. Add bell peppers and snap peas; cook 2–3 minutes more. You want crisp-tender, not soft.
Thicken the sauce. Pour the remaining teriyaki sauce into the pan with the veggies.
Bring to a gentle simmer. Stir in the cornstarch slurry and cook 1–2 minutes, stirring, until glossy and slightly thick.
Combine. Return the chicken and any juices to the pan. Toss to coat everything in the sauce.
Cook 1 minute more. Finish with a squeeze of lime if you like.
Assemble the bowls. Divide rice among four containers. Top with equal portions of teriyaki chicken and veggies.
Sprinkle with sesame seeds and sliced green onions.
Cool, then seal. Let bowls cool on the counter for 15–20 minutes before closing the lids. This helps prevent condensation and keeps textures intact.