Preheat the oven to 375°F (190°C).
Combine the minced garlic and minced ginger and pulse in a food processor or pound with a mortar and pestle until a coarse puree forms.
In a small saucepan, add the soy sauce, water, sweetener, and the garlic‑ginger puree. Simmer gently over low heat until the mixture reduces to about 2/3 cup, tasting occasionally until the flavor is as desired; set aside.
Trim visible fat and any undesirable parts from the chicken breasts. If some breasts are very thick, remove a thin slice from the bottom to even the thickness.
Heat the peanut oil in a large nonstick frying pan over medium‑high heat. Brown the chicken breasts about 3–4 minutes per side until golden but not fully cooked.
Cut each browned chicken breast lengthwise into four even strips (cut larger breasts into five strips if needed so pieces are similar in size).
Arrange the chicken strips in a single layer in the smallest casserole dish that fits them. Brush each piece with about half of the reduced teriyaki sauce.
Bake for 5 minutes, remove and brush generously with more sauce, then return to the oven and bake 5 minutes more.
Remove again, brush with additional sauce, then bake a final 2–5 minutes until the thickest part of the chicken registers 165°F (74°C) on an instant‑read thermometer and the chicken is well glazed.
Serve the hot chicken garnished with thinly sliced green onions if desired. Reheat any extra sauce before serving, if using.