Pat the chicken breast pieces dry with paper towels, then season lightly with salt and pepper. This helps the chicken sear nicely and keeps it juicy.
In a small bowl, whisk together the soy sauce, water or broth, honey, rice vinegar, and sesame oil until smooth. Stir in the garlic and ginger and set aside.
In another small dish, combine the cornstarch with a splash of cold water to make a smooth slurry. This will thicken the teriyaki sauce later.
Heat the neutral oil in a large skillet over medium high heat. Add the seasoned chicken in an even layer and cook, stirring occasionally, until lightly browned and mostly cooked through.
Pour the prepared teriyaki sauce into the skillet and stir to coat all the chicken pieces. Bring the mixture to a gentle simmer.
Drizzle in the cornstarch slurry while stirring constantly. Continue to cook for a few minutes until the sauce becomes thick, glossy, and clings to the chicken.
Turn off the heat and stir in the sliced green onions. Taste and adjust the seasoning with extra honey or vinegar if needed.
Serve the teriyaki chicken hot over cooked rice, sprinkling with sesame seeds and more green onions before serving.