Whisk the low-sodium soy sauce, honey, rice vinegar, minced garlic, fresh ginger, and sesame oil together in a small bowl. In a separate small bowl, combine 1 teaspoon cornstarch with 1 tablespoon cold water until smooth, then whisk the slurry into the teriyaki sauce and set aside.
Pat the chicken pieces thoroughly dry with paper towels. Place them in a medium bowl and sprinkle with the remaining cornstarch. Toss gently until every piece has a very light, even coating.
Heat a large skillet or wok over medium-high heat. Add half of the olive oil and allow it to become hot before adding the chicken. Arrange the chicken in a single layer, working in batches if necessary so the pan does not become overcrowded.
Cook the chicken for approximately 5–7 minutes, turning occasionally, until the pieces are browned on the outside and completely cooked through. Transfer the cooked chicken to a clean plate and keep it nearby while you cook the vegetables.
Add the remaining olive oil to the skillet. Add the broccoli and thinly sliced carrots first and stir-fry for approximately 2–3 minutes. If the pan becomes too dry, add 1–2 tablespoons of water and cover briefly to help the vegetables steam.
Add the sliced bell pepper and snap peas to the skillet. Continue cooking for another 2–3 minutes, stirring frequently, until the vegetables are brightly colored and crisp-tender rather than soft and mushy.
Return the cooked chicken to the skillet with the vegetables. Give the prepared teriyaki sauce a quick stir to redistribute the cornstarch, then pour it evenly over the chicken and vegetables.
Toss everything continuously for 1–2 minutes as the sauce heats and thickens. The sauce should become glossy and coat the chicken and vegetables rather than pooling heavily at the bottom of the skillet.
Stir in the sliced green onions and taste the stir-fry. Add a small splash of rice vinegar for more brightness, red pepper flakes for heat, or a tiny amount of additional honey if you prefer a sweeter teriyaki flavor.
Remove the skillet from the heat and sprinkle the sesame seeds and reserved green onion tops over the finished stir-fry. Serve immediately over steamed rice, cauliflower rice, quinoa, or your preferred side.
For meal prep, divide the stir-fry evenly between four airtight containers. Allow it to cool appropriately before refrigerating, and store the portions in the refrigerator for up to 3–4 days.