Heat 1 tablespoon of olive oil in a large skillet over medium-high heat. Add half of the chicken pieces and sauté for 3–4 minutes until cooked through. Transfer to a plate and repeat with the remaining chicken.
In a small bowl, whisk together teriyaki sauce, water, cornstarch, and honey. This mixture will create a glossy, flavorful coating for the chicken. Set aside while you sauté the vegetables.
Add the remaining olive oil to the skillet, then sauté garlic and ¾ cup of the green onions for about 20 seconds. Toss in diced bell pepper and chopped water chestnuts, cooking for 2 minutes until slightly tender but still crisp.
Pour the sauce into the skillet with the vegetables, stirring constantly for 1 minute until thickened. Add the cooked chicken and shredded carrots, tossing everything together so each piece is coated with the delicious teriyaki glaze.
Spoon the chicken mixture onto lettuce leaves. Sprinkle the remaining green onions and chopped cashews on top for extra flavor and crunch. Serve immediately for best texture.