Preheat the oven to 375°F (190°C).
Puree the minced garlic and minced ginger together using a mortar and pestle, small food processor, or blender until smooth.
Combine soy sauce, water, sweetener, and the garlic-ginger puree in a small saucepan and simmer over low heat, stirring occasionally, until the liquid reduces to about 2/3 cup and is concentrated to your taste.
Trim any visible fat or undesirable bits from the chicken breasts. If some breasts are very thick, trim the bottom edge to even the thickness.
Heat the peanut oil in a large non-stick frying pan over medium-high heat. Brown the chicken breasts about 3–4 minutes per side; they should be browned but not fully cooked through.
Slice each browned chicken breast lengthwise into four even strips (if a breast is much larger, cut into five strips as needed) so pieces are similar in size.
Arrange the chicken strips in a single layer in the smallest casserole or baking dish that will fit them all. Brush the chicken with about half of the reduced teriyaki sauce.
Bake the chicken for about 5 minutes, remove from oven and brush with more sauce. Return to oven and bake another 5 minutes, brush again, then bake an additional 2–5 minutes until an instant-read thermometer inserted into the thickest part reads 165°F (74°C).
When fully cooked and well glazed, serve the chicken hot, garnished with thinly sliced green onions if desired. Reheat any extra sauce separately and serve on the side.
